Anirban Majumdar
@iiitk.ac.in
Assistant Professor, Department of Sciences
IIITDM Kurnool
RESEARCH, TEACHING, or OTHER INTERESTS
Numerical Analysis, Applied Mathematics, Computational Mathematics
Scopus Publications
Scholar Citations
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Scopus Publications
Shree Bala, L. Govindarao, A. Das, and A. Majumdar
Springer Science and Business Media LLC
Anirban Majumdar and Srinivasan Natesan
Wiley
In this article, we devise a uniformly convergent numerical scheme for solving singularly perturbed two‐dimensional parabolic convection–diffusion problem with non‐smooth convection coefficients and source term. The solution of this kind of problem typically exhibits interior layers due to the discontinuity of convection coefficients and source term. To capture the interior layers, the piecewise‐uniform mesh is used in the spatial directions and the uniform mesh is considered in temporal direction. To discretize the temporal and spatial derivatives, we apply an alternating direction method and upwind method, respectively. Theoretically, we prove that the proposed method is ε‐uniformly convergent. Numerical results are presented to demonstrate the theoretical estimates.
Anirban Majumdar and Srinivasan Natesan
Inderscience Publishers
Anirban Majumdar and Srinivasan Natesan
Informa UK Limited
ABSTRACT In this paper, we study the numerical solution of singularly perturbed degenerate parabolic convection–diffusion problem on a rectangular domain. The solution of the problem exhibits a parabolic boundary layer in the neighbourhood of x=0. First, we use the backward-Euler finite difference scheme to discretize the time derivative of the continuous problem on uniform mesh in the temporal direction. Then, to discretize the spatial derivatives of the resulting time semidiscrete problem, we apply the hybrid finite difference scheme, which is a combination of central difference scheme and midpoint upwind scheme on piecewise uniform Shishkin mesh. We derive the error estimates, which show that the proposed hybrid scheme is ϵ-uniform convergent of almost second-order (up to a logarithmic factor) in space and first-order in time. Some numerical results have been carried out to validate the theoretical results.
Anirban Majumdar and Srinivasan Natesan
Springer Science and Business Media LLC
Anirban Majumdar and Srinivasan Natesan
Elsevier BV