Professor & Acting President -SAU
Department of Mathematics
South Asian University
Akbar Bhawan,Room No. 325 Chanakyapuri
New Delhi – 110021,INDIA
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Ph:+91-11-24195294
Profile
Prof Ranjan Kumar Mohanty received his Ph.D degree from the Department of Mathematics, IIT Delhi on the topic ‘Numerical Methods for Partial Differential Equations’, in the year 1990. He is already having more than 30 years of teaching and research experience at University of Indore, University of Delhi and South Asian University. Prof Mohanty is a recipient of prestigious ‘Fulbright-Nehru Senior Research Fellowship 2013’, ‘Commonwealth Fellowship 2000’, and ‘BOYSCAST Fellowship 1996’. He has worked as a post-doctoral fellow at Louisiana Tech University (USA), Nottingham Trent University (UK) and Loughborough University (UK), under the aforesaid fellowship program. He has also visited Technical University Dresden (Germany), University of Strathclyde (Scotland), Nottingham Trent University (England), and Chinese Academy of Sciences Beijing (China) under INSA-DFG, INSA-Royal Society and INSA-CAS bilateral exchange program to carry out advanced research work in his field of research. Prof Mohanty has already published more than 200 research papers in various international academic Journals of repute. To his credit he has successfully guided 27 Ph.D students. He has delivered several lectures as a resource person and invited speakers at different places in India and abroad. He is a regular reviewer of many national and international Journals. Prof Mohanty has been elected as (i) a Fellow of National Academy of Sciencesis (FNASc), in the year 2012, and (ii) a Fellow of Indian Academy of Mathematical Modeling and Simulation (FIAMMS), in the year 2018.
Qualifications
- PhD in Mathematics from Indian Institute of Technology Delhi , in 1990
- M.Sc. in Mathematics from Utkal University, Bhubaneswar , in 1984
Awards & Honours
- Chinese Academy of Sciences (CAS) Fellowship-2019 Awardee, sponsored by The Chinese Academy of Sciences, Beijing and INSA, New Delhi. Research in ‘On the High Order Numerical Methods for Incompressible Fluid Flow Problems’ at the Institute of Computational Mathematics & Scientific/Engineering Computing, Academy of Mathematics & System Science, Chinese Academy of Sciences, Beijing, CHINA ( 24-06-2019 to 21-07-2019).
- Elected, Fellow of the Indian Academy of Mathematical Modeling and Simulation (FIAMMS)-2018
- Royal Society Fellowship Awardee, sponsored by The Royal Society of Edinburgh and INSA, New Delhi. Research in ‘Stability of Numerical Schemes for Second Order Initial Value Problems on Variable Mesh’ at University of Strathclyde, Glasgow, Scotland, U.K. (01-10-2014 to 28-10-2014).
- Fulbright Nehru Senior Research Fellowship 2013 Awardee, sponsored by The United States-India Educational Foundation (USIEF), New Delhi.Research in ‘Computational Fluid Dynamics’ at the Louisiana Tech University, USA . (01-11-2013 to 30-04-2014)
- Elected, Fellow of the National Academy of Sciences, India (FNASc) 2012.
- DFG Fellowship Awardee, sponsored by The Deutsche Forschungsgemeinschaft (The German Research Foundation) under INSA-DFG Bilateral Exchange Programme.Research in ‘High Order Discretizations in Partial Differential Equations and Singular Perturbation’ at the Institute of Numerical Mathematics, Technical University Dresden, Germany. (01-06-2008 to 31-08-2008).
- Royal Society Fellowship Awardee, sponsored by The Royal Society of London under INSA-Royal Society Bilateral Exchange Program.Research in ‘Recent Parallel Computational Methods for Differential Equations’ at The Nottingham Trent University, U.K. (24-03-2004 to 23-06-2004).
- Commonwealth Fellowship Awardee, sponsored by The British Council, London. Research in ‘Applied Numerical Analysis’ at The Nottingham Trent University, U.K. (01-10-2000 to 30-09-2001).
- BOYSCAST Fellowship Awardee, sponsored by the Department of Science and Technology, Government of India.Research in ‘Parallel Computational Methods’ at Loughborough University, U.K. (01-05-1996 to 30-04-1997).
Recent Publications
- R.K. MOHANTY and MD HASAN SARWER, “A Class of Numerical Methods for the Solution of Fourth-Order Non-linear Ordinary Differential Equations on a Graded Mesh with Boundary Conditions of First Kind”, International Journal for Computational Methods in Engineering Science & Mechanics, To appear (2020).
- R.K. MOHANTY and SACHIN SHARMA, “ A new two-level implicit scheme based on cubic spline approximations for the 1D time-dependent quasilinear biharmonic problems”, Engineering with Computers, DOI:10.1007/s00366-019-00778-1,To appear (2020).
- R.K. MOHANTY and BISHNU PADA GHOSH, “Absolute stability of an implicit method based on third-order off-step discretization for the initial-value problem on a graded mesh”, Engineering with Computers, DOI:10.1007/s00366-019-00857-3,To appear (2020).
- R.K. MOHANTY and SACHIN SHARMA, “ Fourth-order accurate method based on half-step cubic spline approximations for the 1D time-dependent quasilinear parabolic partial differential equations”, TWMS Journal of Applied and Engineering Mathematics, To appear (2020).
- R.K. MOHANTY, DEEPTI KAUR and SWARN SINGH, “A class of two- and three-level implicit methods of order two in time and four in space based on half-step discretization for two-dimensional fourth order quasi-linear parabolic equations”, Applied Mathematics and Computations, Vol. 352, pp. 68-87 (2019).
- R.K. MOHANTY and GUNJAN KHURANA, “A new fast algorithm based on half-step discretization for 3D quasilinear hyperbolic partial differential equations”, International Journal of Computational Methods, Vol. 16, ID:1850090 (2019).
- R.K. MOHANTY and GUNJAN KHURANA, “A new high accuracy cubic spline method based on half-step discretization for the system of 1D non-linear wave equations”, Engineering Computations, Vol. 36, pp. 930-957 (2019)
- R.K. MOHANTY and GUNJAN KHURANA, “ A new spline-in-tension method of O(k2+h4) based on off-step grid points for the solution of 1D quasi-linear hyperbolic partial differential equations in vector form”, Differential Equations and Dynamical Systems, Vol.27, pp. 141-168 (2019).
- R.K. MOHANTY, SACHIN SHARMA and SWARN SINGH, “A new two-level implicit scheme for the system of 1D quasi-linear parabolic partial differential equations using spline in compression approximations”, Differential Equations and Dynamical Systems,Vol.27, pp. 327-356 (2019).
- R.K. MOHANTY, GEETAN MANCHANDA and ARSHAD KHAN, “Compact half step approximation in exponential form for 2D second order quasi-linear elliptic partial differential equations”, Journal of Difference Equations and Applications, Vol. 25, pp. 716-749 (2019).
- R.K. MOHANTY and SACHIN SHARMA, “Fourth-order numerical scheme based on half-step non-polynomial spline approximations for 1D quasi-linear parabolic equations”, Numerical Analysis and Applications, To appear (2019).
- R.K. MOHANTY and DEEPTI KAUR, “High accuracy two-level implicit compact difference scheme for 1D unsteady biharmonic problem of first kind: application to generalized Kuramoto-Sivashinsky equation”, Journal of Difference Equations and Applications, Vol. 25, pp. 243-261 (2019).
- V. SINGH, S.U. ISLAM and R. K. MOHANTY, “Local meshless method for convection dominated steady and unsteady partial differential equations”, Engineering with Computers, Vol. 35, pp. 803-812 (2019).
- R.K. MOHANTY, GEETAN MANCHANDA and ARSHAD KHAN, “Operator compact exponential approximation for the solution of the system of 2D second order quasi-linear elliptic partial differential equations”, Advances in Difference Equations, Vol. 2019, ID: 47 (2019).
- DEEPTI KAUR and R.K. MOHANTY, “Two-level implicit high order method based on half-step discretization for 1D unsteady biharmonic problems of first kind”, Applied Numerical Mathematics, Vol. 139, pp. 1-14 (2019).
- R.K. MOHANTY, SACHIN SHARMA and SWARN SINGH, “A new two-level implicit scheme of order two in time and four in space based on half-step spline in compression approximations for unsteady 1D quasi-linearbiharmonic equations”, Advances in Difference Equations, Vol. 2018, ID: 378(2018).
- R.K. MOHANTY and DEEPTI KAUR, “Compact difference scheme with high accuracy for one dimensional unsteady quasi-linear biharmonic problem of second kind: Application to physical problems”, Sibirskii Zhurnal Vychislitel’ noi Matematiki (Numerical Analysis and Applications), Vol. 11, pp. 45-59 (2018).
- R.K. MOHANTY and DEEPTI KAUR, “Unconditionally stable high accuracy compact difference schemes for multi-space dimensional vibration problems with simply supported boundary conditions”, Applied Mathematical Modelling, Vol. 55, pp. 281-298 (2018).
- R.K. MOHANTY and GUNJAN KHURANA, “ A New Fast Numerical Method Based on Off-step Discretization for Two Dimensional Quasilinear Hyperbolic Partial Differential Equations”, International Journal of Computational Methods, Vol. 14, ID:1750031 (2017).
- R.K. MOHANTY, SEAN McKEE and DEEPTI KAUR, “A Class of Two-Level Implicit Unconditionally Stable Methods for a Fourth Order Parabolic Equation”, Applied Mathematics and Computations, Vol. 309, pp. 272-280 (2017).
- R.K. MOHANTY and RAVINDRA KUMAR, “A New Numerical Method Based on Non-Polynomial Spline in Tension Approximations for 1D Quasilinear Hyperbolic Equations on a Variable Mesh”, Differential Equations and Dynamical Systems, Vol. 25, pp. 207-222 (2017).
- R.K. MOHANTY and GUNJAN KHURANA, “A New Spline in Compression Method of Order Four in Space and Two in Time Based on Half-step Grid Points for the Solution of the System of 1D Quasi-linear Hyperbolic Partial Differential Equations”, Advances in Difference Equations, Vol. 2017, ID: 97 (2017).
- N. JHA, R.K. MOHANTY and N. KUMAR, “Compact-FDM for Mildly Nonlinear Two-Space Dimensional Elliptic BVPs in Polar Coordinate System and Its Convergence Theory”, International Journal of Applied and Computational Mathematics, Vol. 3, pp. 255-270 (2017).
- R.K. MOHANTY and DEEPTI KAUR, “High Accuracy Compact Operator Methods for Two-Dimensional Fourth Order Nonlinear Parabolic Partial Differential Equations”, Computational Methods in Applied Mathematics, Vol. 17, pp. 617-641 (2017).
- R.K. MOHANTY and SACHIN SHARMA, “High accuracy quasi-variable mesh method for the system of 1D quasi-linear parabolic partial differential equations based on off-step spline in compression approximations”, Advances in Difference Equations,Vol. 2017, ID: 212 (2017).
- R.K. MOHANTY, SUCHETA NAYAK and ARSHAD KHAN, “Non-Polynomial Cubic Spline Discretization for System of Nonlinear Singular Boundary Value Problems using Variable Mesh”, Advances in Difference Equations, Vol. 2017, ID: 327 (2017).
- R.K. MOHANTY and DEEPTI KAUR, “Numerov Type Variable Mesh Approximations for 1D Unsteady Quasi-linear Biharmonic Problem: Application to Kuramoto-Sivashinsky Equation”, Numerical Algorithms, Vol. 74, pp. 427-459 (2017).
- R.K. MOHANTY and GUNJAN KHURANA, “A Class of Methods for the Numerical Solutions of 3D Multi-Harmonic Elliptic Equations on a Graded Mesh”, Neural Parallel and Scientific Computations, Vol. 24, pp.505-521 (2016).
- R.K. MOHANTY and DEEPTI KAUR, “A Class of Quasi-variable Mesh Methods Based on Off-step Discretization for the Numerical Solution of Fourth-order Quasi-linear Parabolic Partial Differential Equations”, Advances in Difference Equations, Vol. 2016, ID: 326 (2016).
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R.K. MOHANTY, MD HASAN SARWER and NIKITA SETIA, “A Class of Quasi-Variable Mesh Methods Based on Off-Step Discretization for the Solution of Non-linear Fourth Order Ordinary Differential Equations with Dirichlet and Neumann Boundary Conditions”, Advances in Difference Equations,Vol. 2016, ID: 248 (2016).
- JYOTI TALWAR, R.K. MOHANTY and SWARN SINGH, “A New Algorithm Based on Spline in Tension Approximation for 1D Quasilinear Parabolic Equations on a Variable Mesh”, International Journal of Computer Mathematics, Vol. 93, pp.1771-1786 (2016).
- NAVNIT JHA, R.K. MOHANTY and VINOD CHAUHAN, “Efficient Algorithms for Fourth and Sixth Order Two Point Nonlinear Boundary Value Problems using Non polynomial Spline Approximations on a Geometric Mesh”, Computational and Applied Mathematics, Vol. 35, pp. 389-404 (2016).
- R.K. MOHANTY and DEEPTI KAUR, “High Accuracy Implicit Variable Mesh Methods for Numerical Study of Special Types of Fourth Order Non-linear Parabolic Equations”, Applied Mathematics and Computation, Vol. 273, pp. 678-696 (2016).
- M.K. JAIN, SACHIN SHARMA and R.K. MOHANTY, High Accuracy Variable Mesh Method for Nonlinear Two-Point Boundary Value Problems in Divergence Form, Applied Mathematics and Computation, Vol. 273, pp. 885-896 (2016).
- SEAN McKEE, J.A. CUMINATO and R.K. MOHANTY, “On the Convergence of a Finite Difference Scheme for a Second Order Differential Equation Containing Nonlinearly a First Derivative”, Neural Parallel and Scientific Computations, Vol. 24, pp. 269-276 (2016).
- R.K. MOHANTY, WEIZHONG DAI and FEI HAN, “A New High Accuracy Method for Two-dimensional Biharmonic Equation with Nonlinear Third Derivative Terms: Application to Navier-Stokes Equations of Motion”, International Journal of Computer Mathematics, Vol. 92, pp. 1574-1590 (2015).
- R.K. MOHANTY and JYOTI TALWAR, “A New Compact Alternating Group Explicit Iteration Method for the Solution of Nonlinear Time-dependent Viscous Burgers' Equation”, Numerical Analysis and Applications, Vol. 8, pp. 314-328 (2015).
- · R.K. MOHANTY and JYOTI TALWAR, “A New Coupled Reduced Alternating Group Explicit Method for Non-linear Singular Two Point Boundary Value Problems on a Variable Mesh”, Sibirskii Zhurnal Vychislitel’noi Matematiki (Numerical Analysis and Applications), Vol. 8, pp. 55-67 (2015).
- R.K. MOHANTY and JYOTI TALWAR, “A New Coupled Reduced Alternating Group Explicit Method for Non-linear Singular Two Point Boundary Value Problems on a Variable Mesh”, Sibirskii Zhurnal Vychislitel’noi Matematiki (Numerical Analysis and Applications), Vol. 8, pp. 55-67 (2015).
- R.K. MOHANTY and NIKITA SETIA, “A New High Accuracy Two-level Implicit Off-step Discretization for the System of Three Space Dimensional Quasi-linear Parabolic Partial Differential Equations”, Computers and Mathematics with Applications, Vol. 69, pp. 1096-1113 (2015).
- JYOTI TALWAR, R.K. MOHANTY and SWARN SINGH, “A New Spline in Compression Approximation for One Space Dimensional Quasilinear Parabolic Equations on a Variable Mesh”, Applied Mathematics and Computations, Vol. 260, pp. 82-96 (2015).
- R.K. MOHANTY, NAVNIT JHA and RAVINDRA KUMAR, “A New Variable Mesh Method Based on Non-Polynomial Spline in Compression Approximations for 1D Quasilinear Hyperbolic Equations”, Advances in Difference Equations, Vol. 2015, ID: 337 (2015).
- JYOTI TALWAR and R.K. MOHANTY, “A Single Sweep AGE Algorithm based on Off-step Discretization for the Solution of Viscous Burgers' Equation on a Variable Mesh”, Mathematics in Computer Science, Vol. 09, pp. 85-103 (2015).
- R.K. MOHANTY, WEIZHONG DAI and FEI HAN, “Compact Operator Method of Accuracy Two in Time and Four in Space for the Numerical Solution of Coupled Viscous Burgers' Equations”, Applied Mathematics and Computations, Vol. 256, pp. 381-393 (2015).
- JYOTI TALWAR and R.K. MOHANTY, “Coupled Reduced Alternating Group Explicit Algorithm for Third Order Cubic Spline Method on a Non-Uniform Mesh for Nonlinear Singular Two Point Boundary Value Problems”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, Vol. 85, pp. 71-81 (2015).
- R.K. MOHANTY and SEAN McKEE, “On the Stability of Two New Two-step Explicit Methods for the Numerical Integration of Second Order Initial Value Problem on a Variable Mesh”, Applied Mathematics Letters, Vol. 45, pp. 31-36 (2015).
- R.K. MOHANTY, WEIZHONG DAI and DON LIU, “Operator Compact Method of Accuracy Two in Time and Four in Space for the Solution of Time Dependent Burgers-Huxley Equation”, Numerical Algorithms, Vol. 70, pp. 591-605 (2015).
- JYOTI TALWAR and R.K. MOHANTY, “Spline in Tension method for Non-linear Two Point Boundary Value Problems on a Geometric Mesh”, МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ (Mathematical Models and Computer Simulations), Vol. 27, pp. 33-48 (2015).
- R.K. MOHANTY and NIKITA SETIA, “A New Compact Off-step Discretization for the System of 2D Quasi-linear Elliptic Equations on Unequal Mesh”, Computational Mathematics and Modeling, Vol. 25, pp.381-403 (2014).
- R.K. MOHANTY and RAVINDRA KUMAR, “A New Fast Algorithm Based on Half-step Discretization for One Space Dimensional Quasilinear Hyperbolic Equations”, Applied Mathematics and Computations, Vol. 244, pp.624-641 (2014).
- VENU GOPAL, R.K. MOHANTY and L.M. SAHA, “A New High Accuracy Non-polynomial Tension Spline Method for the Solution of One Dimensional Wave Equation in Polar Co-ordinates”, Journal of the Egyptian Mathematical Society, Vol. 22, pp. 280-285 (2014).
- R.K. MOHANTY, SURUCHI SINGH and SWARN SINGH, “A New High Order Space Derivative Discretization for 3D Quasi-linear Hyperbolic Partial Differential Equations”, Applied Mathematics and Computations, Vol. 232, pp.529-541 (2014).
- JYOTI TALWAR and R.K. MOHANTY, “A New Modified Group Explicit Iterative Method for the Numerical Solution of Time Dependent Viscous Burgers’ Equation, International Journal of Modelling, Simulation, and Scientific Computing, Vol. 05, ID: 1350029 (2014).
- R.K. MOHANTY and RAVINDRA KUMAR, “A Novel Numerical Algorithm of Numerov Type for 2D Quasi-linear Elliptic Boundary Value Problems”, International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 15, pp. 473-489 (2014).
- R.K. MOHANTY and JYOTI TALWAR, “A Single Sweep AGE Algorithm on a Variable Mesh based on Off-step Discretization for the Solution of Nonlinear Burgers’ Equation”, Journal of Computational Methods in Physics, Vol. 2014, ID: 853198 (2014).
- R.K. MOHANTY and VENU GOPAL, “High Accuracy Non-polynomial Spline in Compression Method for One-space Dimensional Quasi-linear Hyperbolic Equations with Significant First Order Space Derivative Term”, Applied Mathematics and Computations, Vol. 238, pp.250-265 (2014).
- R.K. MOHANTY, “New High Accuracy Super Stable Alternating Direction Implicit Methods for Two and Three Dimensional Hyperbolic Damped Wave Equations”, Results in Physics, Vol.04, pp. 156-163 (2014).
- NAVNIT JHA and R.K. MOHANTY, “Quintic Hyperbolic Nonpolynomial Spline and Finite Difference Method for Nonlinear Second Order Differential Equations and its Application”, Journal of the Egyptian Mathematical Society, Vol. 22, pp. 115-122 (2014).
- NAVNIT JHA, R.K. MOHANTY and VINOD CHAUHAN, “The Convergence of Geometric Mesh Cubic Spline Finite Difference Scheme for Non-linear Higher Order Two Point Boundary Value Problems”, International Journal of Computational Mathematics, Vol. 2014, ID: 527924 (2014).
- R.K. MOHANTY and VENU GOPAL, “A Fourth Order Finite Difference Method based on Spline in Tension Approximation for the Solution of One-space Dimensional Second Order Quasi-linear Hyperbolic Equations” Advances in Difference Equations, Vol. 2013, ID: 70 (2013).
- R. K. MOHANTY and NIKITA SETIA, “A New Compact High Order Off-step Discretization for the System of 2D Quasi-linear Elliptic Partial Differential Equations”, Advances in Difference Equations, Vol. 2013, ID: 223 (2013).
- SWARN SINGH, SURUCHI SINGH and R.K. MOHANTY, “A New High Accuracy Off-step Discretization for the Solution of 2D Non-linear Triharmonic Equations”, East Asian Journal on Applied Mathematics, Vol. 03, pp. 228-246 (2013).
- R.K. MOHANTY and NIKITA SETIA, “A New High Order Compact Off-step Discretization for the System of 3D Quasi-linear Elliptic Partial Differential Equations”, Applied Mathematical Modelling, Vol. 37, pp. 6870-6883 (2013).
- R.K. MOHANTY and VENU GOPAL, “A New Off-step High Order Approximation for the Solution of Three-space Dimensional Nonlinear Wave Equations”, Applied Mathematical Modelling, Vol. 37, pp. 2802-2815 (2013).
- R.K. MOHANTY, M.K. JAIN and SURUCHI SINGH, “A New Three-level Implicit Cubic Spline Method for the Solution of 1D Quasi-linear Hyperbolic Equations”, Computational Mathematics and Modeling, Vol. 24, pp. 452-470 (2013).
- R.K. MOHANTY , NAVNIT JHA and VINOD CHAUHAN, “Arithmetic Average Geometric Mesh Discretizations for Fourth and Sixth Order Nonlinear Two Point Boundary Value Problems”, Neural Parallel & Scientific Computations, Vol. 21, pp. 393-410 (2013).
- NAVNIT JHA, R.K. MOHANTY and VINOD CHAUHAN, “Geometric Mesh Three Point Discretization for Fourth Order Nonlinear Singular Differential Equations in Polar System”, Advances in Numerical Analysis, Vol. 2013, ID: 614508 (2013).
- NAVNIT JHA, R.K. MOHANTY and VINOD CHAUHAN, “Geometric Mesh Three Point Discretization for Fourth Order Nonlinear Singular Differential Equations in Polar System”, Advances in Numerical Analysis, Vol. 2013, ID: 614508 (2013).
- R.K. MOHANTY, M.K. JAIN and DEEPIKA DHALL, “High Accuracy Cubic Spline Approximation for Two Dimensional Quasi-linear Elliptic Boundary Value Problems”, Applied Mathematical Modelling, Vol. 37, pp. 155-171 (2013).
- VENU GOPAL, R.K. MOHANTY and NAVNIT JHA, “New Non-polynomial Spline in Compression Method of O(k2+h4) for the solution of 1D Wave Equation in Polar Co-ordinates”, Advances in Numerical Analysis, Vol. 2013, ID: 470480 (2013).
- B.N. MISHRA and R.K. MOHANTY, “ Single Cell Numerov Type Discretization for 2D Biharmonic and Triharmonic Equations on Unequal Mesh”, Journal of Mathematical and Computational Science, Vol. 03, pp. 242-253 (2013).
- JYOTI TALWAR and R.K. MOHANTY, “Spline in Compression Method for Non-linear Two Point Boundary Value Problems on a Geometric Mesh”, Neural Parallel & Scientific Computations, Vol. 21, pp. 553-570 (2013).
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R.K. MOHANTY and JYOTI TALWAR, “SWAGE Algorithm for the Cubic Spline Solution of Nonlinear Viscous
Burgers’ Equation on a Geometric Mesh”, Results in Physics. Vol. 03, pp. 195-204 (2013). - JYOTI TALWAR and R.K. MOHANTY, “A Class of Numerical Methods for the Solution of Fourth-Order Ordinary Differential equations in Polar Coordinates”, Advances in Numerical Analysis, Vol. 2012, ID: 626419 (2012).
- R.K. MOHANTY, “A Combind Arithmetic Average Discretization and TAGE Iterative Method for Non-linear Two Point Boundary Value Problems with a Source Function in Integral Form”, Differential Equations and Dynamical Systems, Vol. 20, pp. 423-440 (2012).
- R.K. MOHANTY and JYOTI TALWAR, “A Combined Approach Using Coupled Reduced Alternating Group Explicit (CRAGE) Algorithm and Sixth Order Off-step Discretization for the Solution of Two Point Nonlinear Boundary Value Problems”, Applied Mathematics and Computations, Vol. 219, pp. 248-259 (2012).
- R.K. MOHANTY and NIKITA SETIA, “A New Fourth Order Compact Off-step Discretization for the System of 2D Non-linear Elliptic Partial Differential Equations”, East Asian Journal of Applied Mathematics, Vol. 02, pp. 59-82 (2012).
- R.K. MOHANTY and NIKITA SETIA, “A New High Accuracy Two-level Implicit Off-Step Discretization for the System of Two Space Dimensional Quasi-linear Parabolic Partial Differential Equations”, Applied Mathematics and Computations, Vol. 219, pp. 2680-2697 (2012).
- NIKITA SETIA and R.K. MOHANTY, “A New High Accuracy Variable Mesh Discretization for the Solution of the System of 2D Non-linear Elliptic BoundaryValue Problems”, Neural Parallel & Scientific Computations, Vol. 20, pp. 415-436 (2012).
- R.K. MOHANTY, M.K. JAIN and B.N. MISHRA, “A Novel Numerical Method of O(h4) for Three-dimensional Non-linear Triharmonic Equations”, Communications in Computational Physics, vol. 12, pp. 1417-1433 (2012).
- R.K. MOHANTY and VENU GOPAL, “An Off-step Discretization for the Solution of 1-D Mildly Non-linear Wave Equations with Variable Coefficients”, Journal of Advanced Research in Scientific Computing, Vol. 04, No. 02, pp. 1-13 (2012).
- R.K. MOHANTY, JYOTI TALWAR and NOOPUR KHOSLA, “Application of TAGE Iterative Methods for the Solution of Non-linear Two Point Boundary Value Problems with Linear Mixed Boundary Conditions on a Non-uniform Mesh”, International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 13, pp. 129-134 (2012).
- R.K. MOHANTY and JYOTI TALWAR, “Compact Alternating Group Explicit Method for the Cubic Spline Solution of Two Point Boundary Value Problems with Significant Nonlinear First Derivative Terms”, Mathematical Sciences, Vol. 6,ID: 58 (2012).
- R.K. MOHANTY, RAJIVE KUMAR and VIJAY DAHIYA, “Cubic Spline Iterative Method for Poisson’s Equation in Cylindrical Polar Coordinates”, ISRN Mathematical Physics, Vol. 2012, ID: 234516 (2012).
- R.K. MOHANTY, RAJIVE KUMAR and VIJAY DAHIYA, “Cubic Spline Method for 1D Wave Equation in Polar Coordinates”, ISRN Computational Mathematics, Vol. 2012, ID: 302923 (2012).
- R.K. MOHANTY and VENU GOPAL, “High Accuracy Arithmetic Average Type Discretization for the Solution of Two-space Dimensional Non-linear Wave Equations”, International Journal of Modeling, Simulation, and Scientific Computing, Vol. 03, ID: 1150005 (2012).
- SURUCHI SINGH, SWARN SINGH and R.K. MOHANTY, “High Accuracy Cubic Spline Approximation on a Geometric Mesh for the Solution of 1D Non-linear Wave Equations”, Journal of Mathematical and Computational Science, Vol. 02, pp. 1126-1143 (2012).
- R.K. MOHANTY and SURUCHI SINGH, “High Order Variable Mesh Approximation for the Solution of 1D Non-linear Hyperbolic Equation”, International Journal of Nonlinear Science, Vol. 14, pp. 220-227 (2012).
- JYOTI TALWAR and R.K. MOHANTY, “Smart Alternating Group Explicit (SMAGE) Method for the Cubic Spline Solution of Non-linear Two Point Boundary Value Problems”, Neural Parallel & Scientific Computations, Vol.20, pp. 399-414 (2012).
- R.K. MOHANTY, VIJAY DAHIYA and NOOPUR KHOSLA, “Spline in Compression Methods for Singularly Perturbed 1D Parabolic Equations with Singular Coefficients”, Journal of Discrete Mathematics, Vol. 02, pp. 70-77 (2012).
- R.K. MOHANTY, RAJIVE KUMAR and VIJAY DAHIYA, “Spline in Tension Methods for Singularly Perturbed One Space Dimensional Parabolic Equations with Singular Coefficients”, Neural Parallel & Scientific Computations, Vol. 20, pp. 81-92 (2012).
- R.K. MOHANTY, M.K. JAIN and B.N. MISHRA, “A Compact Discretization of O(h4) for Two-dimensional Non-linear Triharmonic Equations”, Physica Scripta, Vol. 84, ID: 025002 (2011).
- R.K. MOHANTY, M.K. JAIN and DEEPIKA DHALL, “A Cubic Spline Approximation and Application of TAGE Iterative Method for the Solution of Two-Point Boundary Value Problems with Forcing Function in Integral Form”, Applied Mathematical Modelling, Vol. 35, pp. 3036-3047 (2011).
- CHRISTIAN GROSSMANN, R.K. MOHANTY and HANS-GOERG ROOS, “A Direct Higher Order Discretization in Singular Perturbations via Domain Split - A Computational Approach”, Applied Mathematics and Computations, Vol. 217, pp. 9302- 9312 (2011).
- R.K. MOHANTY, M.K. JAIN and B.N. MISHRA, “A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations using Coupled Approach”, American Journal of Computational Mathematics, Vol. 01, pp. 318-327 (2011).
- R.K. MOHANTY and SURUCHI SINGH, “A New High Order Approximation for the Solution of Two-space Dimensional Quasi-linear Hyperbolic Equations”, Advances in Mathematical Physics, Vol. 2011, ID: 420608 (2011).
- R.K. MOHANTY and VIJAY DAHIYA, “An O(k2+kh2+h4) Accurate Two-lelel Implicit Cubic Spline Method for One Space Dimensional Quasi-linear Parabolic Equations”, American Journal of Computational Mathematics, Vol. 01, pp. 11-17 (2011).
- R.K. MOHANTY and SURUCHI SINGH, “High Accuracy Numerov Type Discretization for the Solution of One Space Dimensional Non-linear Wave Equations with Variable Coefficients”, Journal of Advanced Research in Scientific Computing, Vol. 03, No.01, pp. 53-66 (2011).
- R.K. MOHANTY and DEEPIKA DHALL, “High Accuracy Arithmetic Average Discretization for Non-linear Two Point Boundary Value Problems with a Source Function in Integral Form”, Applied Mathematics, Vol. 02, pp.1243-1251 (2011).
- R.K. MOHANTY and VENU GOPAL, “High Accuracy Cubic Spline Finite Difference Approximation for the Solution of One-space Dimensional Non-linear Wave Equations”, Applied Mathematics and Computations, Vol. 218, pp. 4234-4244 (2011).
- NAVNIT JHA and R.K. MOHANTY, “TAGE iterative algorithm and non-polynomial spline basis for the solution of non-linear singular second order ordinary differential equations”, Applied Mathematics and Computations, Vol. 218, pp. 3289-3296 (2011).
- R.K. MOHANTY, “A New High Accuracy Finite Difference Discretization for the Solution of 2D Non-linear Biharmonic Equations Using Coupled Approach”, Numerical Methods for Partial Differential Equations, Vol. 26, pp. 931-944 (2010).
- R.K. MOHANTY, “Application of AGE Method to High Accuracy Variable Mesh Arithmetic Average type Discretization for 1D Non-linear Parabolic Initial Boundary Value Problems”, International Journal for Computational Methods in Engineering Science & Mechanics, Vol. 11, pp. 133-141 (2010).
- R.K. MOHANTY, “On the Use of AGE Algorithm with a New High Accuracy Numerov type Variable Mesh Discretization for 1D Non-linear Parabolic Equations”, Numerical Algorithms, Vol. 54, pp. 379-393 (2010).
- R.K. MOHANTY , “Single Cell Compact Finite Difference Discretizations of Order Two and Four for Multi-dimensional Triharmonic Problems”, Numerical Methods for Partial Differential Equations, Vol. 26, pp. 1420-1426 (2010).
- SWARN SINGH, DINESH KHATTAR and R.K. MOHANTY, “A New Coupled Approach High Accuracy Numerical Method for the Solution of 2D Non-linear Biharmonic Equations”, Neural Parallel and Scientific Computations, Vol. 17, pp. 239-256 (2009).
- DINESH KHATTAR, SWARN SINGH and R.K. MOHANTY, “ A New Coupled Approach High Accuracy Numerical Method for the Solution of 3D Non-linear Biharmonic Equations”, Applied Mathematics and Computations, Vol. 215, pp. 3036-3044 (2009).
- R.K. MOHANTY, “A Variable Mesh C-SPLAGE Method of Accuracy for 1D Nonlinear Parabolic Equations”, Applied Mathematics and Computations, Vol. 213, pp. 79-91 (2009).
- NAVNIT JHA, R.K. MOHANTY and B.K. MISHRA, “Alternating Group Explicit Iterative Method for Non-linear Singular Fredholm Integro-differential Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 86, pp. 1645-1656 (2009).
- R.K. MOHANTY and M.K. JAIN, “High Accuracy Cubic Spline Alternating Group Explicit Methods for 1D Quasi-linear Parabolic Equations”, International Journal of Computer Mathematics, Vol. 86, pp. 1556-1571 (2009).
- R.K. MOHANTY, “New Unconditionally Stable Difference Schemes for the Solution of Multi-dimensional Telegraphic Equations”, International Journal of Computer Mathematics, Vol. 86, pp. 2061-2071 (2009).
- R.K. MOHANTY and DEEPIKA DHALL, “Third Order Accurate Variable Mesh Discretization and Application of TAGE Iterative Method for the Non-linear Two-point Boundary Value Problems with Homogeneous Functions in Integral Form”, Applied Mathematics and Computations, Vol. 215, pp. 2024-2034 (2009).
- R.K. MOHANTY and SWARN SINGH, “A New High Order Two Level Implicit Discretization for the Solution of Singularly Perturbed Three Space Dimensional Non-linear Parabolic Equations”, International Journal of Numerical Analysis and Modelling, Vol. 05, pp. 40-54 (2008).
- R.K. MOHANTY, “A Two-level Implicit Non-uniform Mesh Cubic Spline Method of for the Parabolic Equation ”, Neural Parallel and Scientific Computations, Vol. 16, pp. 449-466 (2008).
- R.K. MOHANTY, NOOPUR KHOSLA and A.K. OJHA, “Arithmetic Average Discretization and Two-step BLAGE Iterative Method for the Solution of Elliptic Partial Differential Equations”, Computing Letters, Vol. 4, pp. 79-90. (2008).
- R.K. MOHANTY and SWARN SINGH, “A New Two Level Implicit Discretization of O(k2+kh2+h4) for the Solution of Singularly Perturbed Two Space Dimensional Non-linear Parabolic Equations”, Journal of Computational and Applied Mathematics, Vol. 208, pp. 391-403 (2007).
- R.K. MOHANTY, SAMIR KARAA and U. ARORA, “An O(k2+kh2+h4) Arithmetic Average Discretization for the solution of 1-D Non-linear Parabolic Equations”, Numerical Methods for Partial Differential Equations, Vol. 23, pp. 640-651 (2007).
- R.K. MOHANTY, “An Implicit High Accuracy Variable Mesh Scheme for 1-D Non-linear Singular Parabolic Partial Differential Equations”, Applied Mathematics and Computations, Vol. 186, pp. 219-229 (2007).
- P.K. PANDEY and R.K. MOHANTY, “An Order h4 Numerical Technique for solving Biharmonic Equation”, Neural Parallel and Scientific Computations, Vol. 15, pp. 59-74 (2007).
- R.K. MOHANTY, “Stability Interval for Explicit Difference Schemes for Multi-dimensional Second Order Hyperbolic Equations with Significant First Order Space Derivative Terms”, Applied Mathematics and Computations, Vol. 190, pp.1683-1690 (2007).
- R.K. MOHANTY, “ The Smart-BLAGE Algorithm for Singularly Perturbed 2D Elliptic Partial Differential Equations”, Applied Mathematics and Computations, Vol. 190, pp. 321-331 (2007).
- R.K. MOHANTY, “Three-step BLAGE Iterative Method for Two-dimensional Elliptic Boundary Value Problems with Singularity”, International Journal of Computer Mathematics, Vol. 84, pp. 1613 – 1624 (2007).
- U. ARORA, SAMIR KARAA and R.K. MOHANTY, “A New Stable Variable Mesh Method for 1-D Non-linear Parabolic Partial Differential Equations”, Applied Mathematics and Computations, Vol. 181, pp. 1423-1430 (2006).
- R.K. MOHANTY, “A Class of Non-Uniform Mesh Three Point Arithmetic Average Discretization for and the Estimates of ”, Applied Mathematics and Computations, Vol. 183, pp. 477-485 (2006).
- R.K. MOHANTY and U. ARORA, “A Family of Non-uniform Mesh Tension Spline Methods for Singularly Perturbed Two Point Singular Boundary Value Problems with Significant First Derivatives”, Applied Mathematics and Computations, Vol. 172, pp. 531-544 (2006).
- R.K. MOHANTY and SWARN SINGH, “A New Fourth Order Discretization for Singularly Perturbed Two Dimensional Non-linear Elliptic Boundary Value Problems”, Applied Mathematics and Computations, Vol. 175, pp. 1400-1414 (2006).
- R.K. MOHANTY and SWARN SINGH, “A New Highly Accurate Discretization for Three Dimensional Singularly Perturbed Non-linear Elliptic Partial Differential Equations”, Numerical Methods for Partial Differential Equations, Vol. 22, pp. 1379-1395 (2006).
- R.K. MOHANTY, D.J. EVANS and NAVNIT JHA, “A Sixth Order Accurate AGE Iterative Method for Non-linear Singular Two Point Boundary Value Problems”, Journal of Computational Methods in Science and Engineering, Vol. 06, pp. 57-69 (2006).
- R.K. MOHANTY and U. ARORA, “A TAGE Iterative Method for the Solution of Non-linear Singular Two Point Boundary Value Problems using a Sixth Order Discretization”, Applied Mathematics and Computations, Vol. 180, pp. 538-548 (2006).
- R.K. MOHANTY and NOOPUR KHOSLA, “Application of TAGE Iterative Algorithms to an Efficient Third Order Arithmetic Average Variable Mesh Discretization for Two Point Non-linear Boundary Value Problems”, Applied Mathematics and Computations, Vol. 172, pp. 148-162 (2006).
- R.K. MOHANTY, “Comparison of TAGE and SOR Methods for Variable Mesh Arithmetic Average Discretization for Non-linear Two Point Boundary Value Problems with Mixed Boundary Conditions”, International Journal of Applied Mathematics & Statistics, Vol. 06, pp. 87-100 (2006).
- R.K. MOHANTY, SAMIR KARAA and U. ARORA, “Fourth Order Nine Point Unequal Mesh Discretization for the Solution of 2D Nonlinear Elliptic Partial Differential Equations”, Neural Parallel and Scientific Computations, Vol. 14, pp. 453-470 (2006).
- R.K. MOHANTY and NAVNIT JHA, “A Class of Variable Mesh Spline in Compression Methods for Singularly Perturbed Two Point Singular Boundary Value Problems”, Applied Mathematics and Computations, Vol. 168, pp. 704-716 (2005).
- R.K. MOHANTY, “A Family of Variable Mesh Methods for the Estimates of (du/dr) and the Solution of Non-linear Two Point Boundary Value Problems with Singularity”, Journal of Computational and Applied Mathematics, Vol. 182, pp. 173-187 (2005).
- R.K. MOHANTY and NOOPUR KHOSLA, “A Third Order Accurate Variable Mesh TAGE Iterative Method for the Numerical Solution of Two Point Non-linear Singular Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 82, pp. 1261-1273 (2005).
- R.K. MOHANTY and D.J. EVANS, “Alternating Group Explicit Parallel Algorithms for the Solution of One Space Dimensional Non-linear Singular Parabolic Equations using an O(k2+h4) Difference Method”, International Journal of Computer Mathematics, Vol. 82, pp. 203-218 (2005).
- R.K. MOHANTY, D.J. EVANS and NOOPUR KHOSLA, “An Non-uniform Mesh Cubic Spline TAGE Method for Non-linear Singular Two-point Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 82, pp.1125-1139 (2005).
- R.K. MOHANTY, “An Operator Splitting Technique for an Unconditionally Stable Difference Method for a Linear Three Space Dimensional Hyperbolic Equation with Variable Coefficients”, Applied Mathematics and Computations, Vol. 162, pp. 549-557 (2005).
- R.K. MOHANTY, “An Unconditionally Stable Finite Difference Formula for a Linear Second Order One Space Dimensional Hyperbolic Equation with Variable Coefficients”, Applied Mathematics and Computations, Vol. 165, pp. 229-236 (2005)
- R.K. MOHANTY, D.J. EVANS and U. ARORA, “Convergent Spline in Tension Methods for Singularly Perturbed Two Point Singular Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 82, pp. 55-66 (2005).
- R.K. MOHANTY and D.J. EVANS, “Highly Accurate Two Parameter CAGE Parallel Algorithms for Non-linear Singular Two Point Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 82, pp. 433-444 (2005).
- R.K. MOHANTY and SWARN SINGH, “Non-uniform Mesh Arithmetic Average Discretization for Parabolic Initial Boundary Value Problems”, Neural Parallel and Scientific Computations, Vol. 13, pp. 411-426 (2005).
- D.J. EVANS and R.K. MOHANTY, “On the Application of the SMAGE Parallel Algorithms on a Non-uniform Mesh for the Solution of Non-linear Two Point Boundary Value Problems with Singularity”, International Journal of Computer Mathematics, Vol. 82, pp. 341-353 (2005).
- R.K. MOHANTY, P.L. SACHDEV and NAVNIT JHA, “An O(h4) Accurate Cubic Spline TAGE Method for Non-linear Singular Two Point Boundary Value Problems”, Applied Mathematics and Computations, Vol. 158, pp. 853-868 (2004).
- R.K. MOHANTY, “An Operator Splitting Method for an Unconditionally Stable Difference Scheme for a Linear Hyperbolic Equation with Variable Coefficients in Two Space Dimensions”, Applied Mathematics and Computations, Vol. 152, pp. 799 – 806 (2004).
- R.K. MOHANTY, “An Unconditionally Stable Difference Scheme for the One Space Dimensional Linear Hyperbolic Equation”, Applied Mathematics Letters, Vol. 17, pp. 101-105 (2004).
- R.K. MOHANTY and D.J. EVANS, “Fourth Order Accurate BLAGE Iterative Method for the Solution of Two Dimensional Elliptic Equation in Polar Coordinates”, International Journal of Computer Mathematics, Vol. 81, pp. 1537-1548 (2004).
- R.K. MOHANTY, NAVNIT JHA and D.J. EVANS, “Spline in Compression Method for the Numerical Solution of Singularly Perturbed Two Point Singular Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 81, pp. 615-627 (2004).
- R.K. MOHANTY and D.J. EVANS, “A Fourth Order Accurate Cubic Spline Alternating Group Explicit Method for Non-linear Singular Two Point Boundary Value Problems”, International Journal of Computer Mathematics, Vol. 80, pp. 479-492 (2003)
- R.K. MOHANTY, “A Two-level Implicit Difference Formula of O(k2+h4) for the Numerical Solution of One Space Dimensional Unsteady Quasi-linear Biharmonic Problem of First Kind”, Journal of Computational Methods in Science and Engineering, Vol. 3, pp. 193-208 (2003).
- R.K. MOHANTY, “An Accurate Three Spatial Grid Point Discretization of O(k2+h4) for the Numerical Solution of One Space Dimensional Unsteady Quasi-linear Biharmonic Problem of Second Kind”, Applied Mathematics and Computations, Vol. 140, pp. 1-14 (2003).
- R.K. MOHANTY, D.J. EVANS and DINESH KUMAR, “High Accuracy Difference Formulae for a Fourth Order Quasi-linear Parabolic Initial Boundary Value Problem of First Kind”, International Journal of Computer Mathematics, Vol. 80, pp. 381-398 (2003).
- R.K. MOHANTY, DINESH KUMAR and M.K. JAIN, “Single Cell Discretization of O(kh2+h4) for (u/n) for Three Space Dimensional Mildly Quasi-linear Parabolic Equation”, Numerical Methods for Partial Differential Equations, Vol. 19, pp. 327-342 (2003).
- R.K. MOHANTY, P.L. SACHDEV and NAVNIT JHA, “TAGE Method for Non-linear Singular Two Point Boundary Value Problem using a Fourth Order Difference Scheme”, Neural Parallel and Scientific Computations, Vol. 11, pp. 281-297 (2003).
- R.K. MOHANTY and D.J. EVANS, “The Numerical Solution of Fourth Order Mildly Quasi-linear Parabolic Initial Boundary Value Problem of Second Kind”, International Journal of Computer Mathematics, Vol. 80, pp. 1147-1159 (2003)
- R.K. MOHANTY and URVASHI ARORA, “ A New Discretization Method of Order Four for the Numerical Solution of One Space Dimensional Second Order Quasi-linear Hyperbolic Equation”, International Journal of Mathematical Education in Science and Technology, Vol. 33, pp. 829-838 (2002).
- D.J. EVANS and R.K. MOHANTY, “Alternating Group Explicit Method for the Numerical Solution of Non-linear Singular Two Point Boundary Value Problems using a Fourth Order Finite Difference Method”, International Journal of Computer Mathematics, Vol. 79, pp. 1121-1133 (2002).
- R.K. MOHANTY, M.K. JAIN and URVASHI ARORA, “An Unconditionally Stable ADI Method for the Linear Hyperbolic Equation in Three Space Dimensions”, International Journal of Computer Mathematics, Vol. 79, pp. 133-142 (2002).
- R.K. MOHANTY and SHIVANI DEY, “A New Finite Difference Discretization of Order Four for (u/n) for Two Dimensional Quasi-linear Elliptic Boundary Value Problem”, International Journal of Computer Mathematics, Vol. 76, pp. 505-516 (2001).
- R.K. MOHANTY and M.K. JAIN, “An Unconditionally Stable Alternating Direction Implicit Scheme for the Two Space Dimensional Linear Hyperbolic Equation”, Numerical Methods for Partial Differential Equations, Vol. 17, pp. 684-688 (2001).
- R.K. MOHANTY, D.J. EVANS and P.K. PANDEY, “Block Iterative Methods for the Numerical Solution of Three Dimensional Mildly Non-linear Biharmonic Problems of First Kind”, International Journal of Computer Mathematics, Vol. 77, pp. 319-332 (2001).
- R.K. MOHANTY, URVASHI ARORA and M.K. JAIN, “Fourth Order Approximation for the Three Space Dimensional Certain Mildly Quasi-linear Hyperbolic Equation”, Numerical Methods for Partial Differential Equations, Vol. 17, pp. 277-289 (2001).
- R.K. MOHANTY, URVASHI ARORA and M.K. JAIN, “Linear Stability Analysis and Fourth Order Approximations at First Time Level for the Two Space Dimensional Mildly Quasi-linear Hyperbolic Equations”, Numerical Methods for Partial Differential Equations, Vol. 17, pp. 607-618 (2001).
- R.K. MOHANTY, M.K. JAIN and DINESH KUMAR, “Single Cell Discretization of O(kh2+h4) for the Estimates of (u/n) for Two Space Dimensional Quasi-linear Parabolic Equation”, Numerical Methods for Partial Differential Equations, Vol. 17, pp. 250-261 (2001).
- R.K. MOHANTY, D.J. EVANS and SHIVANI DEY, “Three Point Discretization of Order Four and Six for (du/dx) of the Solution of Non-linear Singular Two Point Boundary Value Problem”, International Journal of Computer Mathematics, Vol. 78, pp. 123-139 (2001).
- R.K. MOHANTY, “A Fourth Order Finite Difference Method for the General One-Dimensional Non-linear Biharmonic Problems of First Kind”, Journal of Computational and Applied Mathematics, Vol. 114, pp. 275-290 (2000).
- R.K. MOHANTY, M.K. JAIN and DINESH KUMAR, “Single Cell Finite Difference Approximations of O(kh2+h4) for (u/x) for One Space Dimensional Non-linear Parabolic Equations”, Numerical Methods for Partial Differential Equations, Vol. 16, pp. 408-415 (2000).
- R.K. MOHANTY and SHIVANI DEY, “Single Cell Fourth Order Difference Approximations for (u/x), (u/y) and (u/z) of the Three Dimensional Quasi-linear Elliptic Equation”, Numerical Methods for Partial Differential Equations, Vol.16, pp. 417-425 (2000).
- R.K. MOHANTY and D.J. EVANS, “Block Iterative Methods for One Dimensional Non-linear Biharmonic Problems on a Parallel Computer”, Parallel Algorithms and Applications, Vol. 13, pp. 239-263 (1999).
- R.K. MOHANTY and D.J. EVANS, “ New Algorithms for the Numerical Solution of One Dimensional Singular Biharmonic Problems of Second Kind ”, International Journal of Computer Mathematics, Vol. 73, pp. 105-124 (1999).
- D.J. EVANS and R.K. MOHANTY, “Block Iterative Methods for the Numerical Solution of Two Dimensional Non-linear Biharmonic Equations”, International Journal of Computer Mathematics, Vol. 69, pp. 371-390 (1998).
- R.K. MOHANTY and P.K. PANDEY, “Families of Accurate Discretizations of Order Two and Four for 3-D Mildly Non-linear Biharmonic Problems of Second Kind”, International Journal of Computer Mathematics, Vol. 68, pp. 363-380 (1998).
- R.K. MOHANTY, M.K. JAIN and K. GEORGE, “Fourth Order Approximations at First Time Level, Linear Stability Analysis and the Numerical Solution of Multi-Dimensional Second Order Non-linear Hyperbolic Equations in Polar Coordinates”, Journal of Computational and Applied Mathematics, Vol. 93, pp. 1-12 (1998).
- R.K. MOHANTY, “High Accuracy Difference Schemes for a Class of Three Space Dimensional Singular Parabolic Equations with Variable Coefficients”, Journal of Computational and Applied Mathematics, Vol. 89, pp. 39-51 (1997).
- R.K. MOHANTY, “Order h4 Difference Methods for a Class of Singular Two Space Elliptic Boundary Value Problems”, Journal of Computational and Applied Mathematics, Vol. 81, pp. 229-247 (1997).
- R.K. MOHANTY, “An O(k2 + h4) Finite Difference Method for One Space Burgers Equation in Polar Coordinates”, Numerical Methods for Partial Differential Equations, Vol. 12, pp. 579-583 (1996).
- R.K. MOHANTY and P.K. PANDEY, “Difference Methods of Order Two and Four for Systems of Mildly Non-linear Biharmonic Problems of the Second Kind in Two Space Dimensions”, Numerical Methods for Partial Differential Equations, Vol. 12, pp. 707-717 (1996).
- R.K. MOHANTY, M.K. JAIN and P.K. PANDEY, “Finite Difference Methods of Order Two and Four for 2-D Non-linear Biharmonic Problems of First Kind”, International Journal of Computer Mathematics, Vol. 61, pp. 155-163 (1996).
- R.K. MOHANTY and M.K. JAIN, “High Accuracy Difference Schemes for the System of Two space Non-linear Parabolic Differential Equations with Mixed Derivatives and Variable Coefficients”, Journal of Computational and Applied Mathematics, Vol. 70, pp. 15-32 (1996).
- R.K. MOHANTY, M.K. JAIN and K. GEORGE, “High Order Difference Schemes for the System of Two Space Second Order Non-linear Hyperbolic Equations with Variable Coefficients”, Journal of Computational and Applied Mathematics, Vol. 70, pp. 231-243 (1996).
- R.K. MOHANTY, M.K. JAIN and K. GEORGE, “On the Use of High Order Difference Methods for the System of One Space Second Order Non-linear Hyperbolic Equations with Variable Coefficients”, Journal of Computational and Applied Mathematics, Vol. 72, pp. 421-431 (1996).
- R.K. MOHANTY and M.K. JAIN, “The Numerical Solution of the System of 3-D Non-linear Elliptic Equation with Mixed Derivatives and Variable Coefficients using Fourth Order Difference Methods”, Numerical Methods for Partial Differential Equations, Vol. 11, pp. 187-197 (1995).
- R.K. MOHANTY and M.K. JAIN, “Fourth Order Operator Splitting Method for the Three Space Parabolic Equation with Variable Coefficients”, International Journal of Computer Mathematics, Vol. 50, pp. 55-64 (1994).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “Fourth Order Finite Difference Method for 2-D Parabolic Partial Differential Equations with Non-linear First Derivative Terms”, Numerical Methods for Partial Differential Equations, Vol. 8, pp. 21-31 (1992).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “Fourth Order Finite Difference Method for Three Dimensional Elliptic Equations with Non-linear First Derivative Terms”, Numerical Methods for Partial Differential Equations, Vol. 8, pp. 575-591 (1992).
- R.K. MOHANTY, “Fourth Order Finite Difference Methods for the System of 2-D Non-linear Elliptic Equations with Variable Coefficients”, International Journal of Computer Mathematics, Vol. 46, pp. 195-206 (1992).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “High Order Difference Methods for the System of One Dimensional Second Order Hyperbolic Equations with Non-linear First Derivative Terms”, Journal of Mathematical and Physical Sciences, Vol. 26, pp. 401-411 (1992).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “A Higher Order Difference Method for 3-D Parabolic Partial Differential Equations with Non-linear First Derivative Terms”, International Journal of Computer Mathematics, Vol. 38, pp. 101-112 (1991).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “Fourth Order Difference Methods for the System of 2-D Non-linear Elliptic Partial Differential Equations”, Numerical Methods for Partial Differential Equations, Vol. 7, pp. 227-244 (1991).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “The Numerical Solution of the Two Dimensional Unsteady Navier-Stokes’ Equations using Fourth Order Difference Method”, International Journal of Computer Mathematics, Vol. 39, pp. 125-134 (1991).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “A Fourth Order Difference Method for the One Dimensional General Quasi-linear Parabolic Partial Differential Equation”, Numerical Methods for Partial Differential Equations, Vol. 6, pp. 311-319 (1990).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “High Order Difference Methods for System of 1-D Non-linear Parabolic Partial Differential Equations”, International Journal of Computer Mathematics , Vol. 37, pp. 105-112 (1990).
- M.K. JAIN, R.K. JAIN and R.K. MOHANTY, “A Fourth Order Difference Method for Elliptic Equations with Non-linear First Derivative Terms”, Numerical Methods for Partial Differential Equations, Vol. 5, pp. 87-95 (1989).
Research Interests
- Computational Fluid Dynamics; Numerical Methods based on Splines, Galerkin, Collocation, Finite Difference, Finite Element, Spectral, Finite Volume, etc. for the solution of quasi-linear PDEs.