Publications
Referred Journals
(1) “A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection-diffusion problem”, with Mohan K. Kadalbajoo and Ashish Awasthi, Journal of Computational and Applied Mathematics, 220 (2008) 271-289.
(2) “Numerical solution of singularly perturbed convection-diffusion problem using parameter uniform B-spline collocation method”, with Mohan K. Kadalbajoo, Journal of Mathematical Analysis and Applications, 355 (2009) 439-452.
(3) “A parameter uniform B-spline collocation method for solving singularly perturbed turning point problem having twin boundary layers”, with Mohan K. Kadalbajoo, International Journal of Computer Mathematics, 87 (2010) 3218-3235.
(4) “A layer adaptive B-spline collocation method for singularly perturbed one-dimensional parabolic problem with a boundary turning point”, with Mohan K. Kadalbajoo, Numerical Methods for Partial Differential Equations, 27 (2011) 1143-1164.
(5) “Numerical approximation of modified Burgers’ equation via hybrid finite difference scheme on layer-adaptive mesh”, with Mohan K. Kadalbajoo, Neural Parallel and Scientific Computations, 18 (2010) 167-194.
(6) “Hybrid finite difference methods for solving modified Burgers and Burgers-Huxley equations”, with Mohan K. Kadalbajoo, Neural Parallel and Scientific Computations, 18 (2010) 409-422.
(7) “A singular perturbation approach to solve Burgers-Huxley equation via hybrid finite difference scheme on layer-adaptive mesh”, with Mohan K. Kadalbajoo, Communications in Nonlinear Science and Numerical Simulation, 16 (2011) 1825-1844.
(8) “A brief survey on numerical methods for solving singularly perturbed problems”, with Mohan K. Kadalbajoo, Applied Mathematics and Computation, 217 (2010) 3641-3716.
(9) “Collocation method using artificial viscosity for solving stiff singularly perturbed turning point problem having twin boundary layers”, with Mohan K. Kadalbajoo and Puneet Arora, Computers & Mathematics with Applications 61 (2011) 1595-1607.
(10) “Qualitative analysis and numerical solution of burgers’ equation via B-spline collocation with implicit euler method on piecewise uniform mesh”, with Mohan K. Kadalbajoo, Journal of Numerical Mathematics. 24 (2016) 73-94.
(11) “Local maximum principle satisfying high order non-oscillatory schemes”, with Ritesh Kumar and Biswarup Biswas, International Journal for Numerical Methods in Fluids. 81(11) (2016) 689-715.
(12) “Higher order numerical approximation for time dependent singularly perturbed differential-difference convection-diffusion equations”, with Mukesh Kumar & Sunil Kumar, Numerical Methods for Partial Differential Equations. 34(1) (2018) 357-380.
(13) “A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters”, with Ritesh Kumar & Mohan K. Kadalbajoo, International Journal of Computer Mathematics. 96(3) (2019) 474-499.
(14) “A Mesh Refinement Algorithm for Singularly Perturbed Boundary and Interior Layer Problems ”, with Ritesh Kumar, International Journal of Computational Methods. 17 (07) (2020), 1950024
(15) “Second-order parameter-uniform finite difference scheme for singularly perturbed parabolic problem with a boundary turning point ”, with Sanjay K. Sahoo, Journal of Difference Equations and Applications. 27(2) (2021), 223-240
(16) “Robust higher order finite difference scheme for singularly perturbed turning point problem with two outflow boundary layers ”, with Sanjay K. Sahoo and Ritesh Dubey, Computational and Applied Mathematics. 40, 179 (2021).
(17) “A mesh adaptation algorithm using new monitor and estimator function for discontinuous and layered solution'', with Prabhat Mishra and Ritesh Dubey, Numerical Algebra, Control and Optimization. 12(3) (2022) 637–658.
(18) "An application of variational iteration method for solving fuzzy time-fractional diffusion equations", with Saurabh Kumar, Neural Computing and Applications. 33 (2021) 17659–17668.
(19) ``Higher order robust numerical computation for singularly perturbed problem involving discontinuous convective and source term", with Sanjay K. Sahoo, Mathematical methods in the Applied Sciences 45(8) (2022) 4876–4898.
(20) ``An approach based on fractional-order Lagrange polynomials for the numerical approximation of fractional order non-linear Volterra-Fredholm integro-differential equations", with Saurabh Kumar, Journal of Applied Mathematics & Computing. 69, (2022) 251–272.
(21) ``An efficient operational matrix technique to solve the fractional order non‑local boundary value problems", with Saurabh Kumar and JF Gómez‑Aguilar, Journal of Mathematical Chemistry. 60 (2022) 1463–1479.
(22) “A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem”, with Sanjay K. Sahoo, Computers and Mathematics with Applications. 137 (2023) 126–146.
(23) “An accurate operational matrix method based on Lagrange polynomials for solving fractional-order pantograph delay and Riccati differential equations”, with Saurabh Kumar, Ajay Kumar and JF Gómez-Aguilar, Physica Scripta. 98(4) (2023) 044005.
(24) “An almost second-order robust computational technique for singularly perturbed parabolic turning point problem with an interior layer”, with Sanjay K. Sahoo, Mathematics and Computers in Simulation. 211 (2023) 192–213.
(25) “Parameter robust higher-order finite difference method for convection-diffusion problem with time delay”, with Sanjay K. Sahoo, Numerical Methods for Partial Differential Equations. 39 (6) (2023) 4145-4143.
(26) ``A robust higher-order finite difference technique for a time-fractional singularly perturbed problem", with Sanjay K. Sahoo, Mathematics and Computers in Simulation. 215 (2024) 43–68.
(27) ``Collocation method with Lagrange polynomials for variable-order time-fractional advection-diffusion problems", with Saurabh Kumar, Mathematical methods in the Applied Sciences (Accepted)
Conference Papers
(1) “A parameter free numerical method for solving singularly perturbed turning point problem having two boundary layers on a non-uniform mesh”, with Mohan K. Kadalbajoo, presented in International Conference on Computational, Mathematical and Statistical Methods, Jan. 6-8, 2007, IIT Madras, India.
(2) “A uniformly convergent B-spline collocation technique on a non-uniform mesh for solving singularly perturbed turning point problem exhibiting two boundary layers”, with Mohan K. Kadalbajoo, presented in Computational and Mathematical Methods in Science and Engineering, 7th International conference, June 20-23, 2007, Illinois Institute of Technology, Chicago, Illinois, USA.
(3) “A layer adaptive B-spline collocation method for singularly perturbed one-dimensional parabolic problem with a boundary turning point”, with Mohan K. Kadalbajoo, presented in 73rd Annual Conference of the Indian Mathematical Society, Dec. 27-30, 2007, University of Pune, Pune, India.
(4) “A Hybrid Finite Difference Scheme with Shishkin Mesh for Solving Singularly Perturbed One-Dimensional Parabolic Problems”, with Mohan K. Kadalbajoo, presented in The 6th International Conference On Differential Equations and Dynamical Systems, May 22-26, 2008, Morgan State University, Baltimore, Maryland, USA.
(5) “A uniformly convergent hybrid finite difference scheme for two-parameter singularly perturbed parabolic problem”, with Mohan K. Kadalbajoo, presented in 28th Annual Southeastern Atlantic Regional Conference on Differential Equations, Oct. 10-11, 2008, University of Arkansas at Little Rock, Little Rock, Arkansas, USA.
(6) “Numerical solution of Burgers’ equation via B-spline collocation method on a layer adaptive mesh”, with Mohan K. Kadalbajoo, presented in International Conference on Applied Mathematics and Approximation Theory, Oct. 11-13, 2008, University of Memphis, Memphis, Tennessee, USA.
(7) “A higher order monotone finite difference operator to solve modified Burgers’ equation on a piecewise equidistant mesh”, with Mohan K. Kadalbajoo, presented in National Meet of Research Scholars in Mathematical Sciences, Dec. 6-10, 2008, Indian Institute of Technology, Kanpur, India.
(8) “A higher order parameter uniform scheme for solving singularly perturbed parabolic problems with small parameters”, with Mohan K. Kadalbajoo, presented in Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations, May 7-9, 2009, Mississippi State University, Mississippi State, MS, USA.
(9) “Hybrid Finite Difference Methods for Solving Modified Burgers and Burgers-Huxley Equations”, with Mohan K. Kadalbajoo, presented in The Fourth International Conference on Neural Parallel and Scientific Computations, August 11-14, 2010, Morehouse college, Atlanta, Georgia, USA.
(10) “Hybrid Finite Difference Methods for Solving Burgers-Huxley Equations”, with Mohan K. Kadalbajoo, presented in Coloquios Semanales, October 13, 2010, Departamento de Ingenieria Matematica, Universidad de Concepcion, Concepcion, Chile
(11) “Second order finite difference scheme for time dependent singularly perturbed differential-difference convection-diffusion problem”, presented in International Conference on Current Trends in PDEs: Theory & Computations, Dec. 28-30, 2015, South Asian University, New Delhi, India.
(12) “Higher order numerical scheme for singularly perturbed differential-difference convection-diffusion problem”, presented in International Conference on Mathematical Modelling Differential Equations, Scientific Computing & Applications, March 27-29, 2016, IIT Kanpur, India.
(13) “Second order finite difference scheme for time dependent singularly perturbed problem with two small parameters”, presented in International Conference on Recent Advances in Theoretical & Computational Partial Differential Equations with Applications December 05-09, 2016, Panjab University, Chandigarh, India.
(14) “Higher order fitted mesh finite difference scheme for singularly perturbed turning point problem”, presented in International Conference on Current Trends in Theoretical and Computational Differential Equations with Applications Dec. 01-05, 2017, South Asian University, New Delhi, India.
(15) “Second order parameter-uniform finite difference scheme for singularly perturbed parabolic problem with a boundary turning point”, presented in 4-th International Conference on Recent Developments in Theory, Computation & Applications Jan. 21-23, 2019, South Asian University, New Delhi, India.
(16) “Higher order numerical scheme for Singularly perturbed problem with an interior turning point”, presented in 2nd International Conference on Mathematical Modelling, Applied Analysis and Computation August. 08-10, 2019, JECRC University, Jaipur, India.
(17) ``Higher Order Uniformly Convergent Finite Difference Scheme For Singularly perturbed Parabolic Problem With A Boundary Turning Point", presented in 3rd International conference on Mathematical Modelling, Applied Analysis and Computation-2020 (ICMMAAC-20) during 7-9 August, 2020, JECRC University
(18) “Higher Order Uniformly Convergent Finite Difference Scheme for Singularly Perturbed Parabolic Problem with a Boundary Turning Point”, presented in International Conference on Computational Sciences-Modelling, Computing and Soft Computing CSMCS-2020, Sept. 10-12, 2020, NIT Calicut
(19) “Higher order numerical scheme for singularly perturbed problem with an interior turning point” presented in National Symposium on Current Trends in Numerical Methods for PDEs, January 16, 2022, IIT Kanpur.
(20) “A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem” presented in 5th International Conference on Mathematical Modelling, Applied Analysis and Computation-2022 (ICMMAAC-22), 04-06 August, 2022, JECRC University, Jaipur.