USSR Computational Mathematics and Mathematical Physics
Applied Numerical Mathematics
A uniformly convergent scheme on a nonuniform mesh for convection-diffusion parabolic problems
Journal of Computational and Applied Mathematics
Singularly perturbed parabolic problems with non-smooth data
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems
Neural, Parallel & Scientific Computations
Mathematical and Computer Modelling: An International Journal
A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems
Neural, Parallel & Scientific Computations
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In this article, a class of singularly perturbed parabolic initial-boundary-value problems possessing strong interior layer due to discontinuous convection coefficient are considered. To solve these problems, we propose a numerical scheme which comprises of classical backward-Euler method tor the time discretization and a hybrid finite difference scheme (which is a proper combination of the midpoint upwind scheme in the outer regions and the classical central difference scheme in the interior layer regions) for the spatial discretization. Computationally we show that the proposed numerical scheme is uniformly convergent with respect to the singular perturbation parameter. This is accomplished by constructing a special rectangular mesh involving a piecewise-uniform Shishkin mesh for the spatial variable. Further, we show higher order accuracy of the proposed scheme by comparing it with a classical implicit upwind finite difference scheme.