Volume 41, pp. 376-395, 2014.

A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems on equidistributed grids

S. Gowrisankar and Srinivasan Natesan

Abstract

In this article, we propose a parameter-uniform computational technique to solve singularly perturbed delay parabolic initial-boundary-value problems exhibiting parabolic boundary layers. The domain is discretized by a uniform mesh in the time direction and a nonuniform mesh for the spatial variable obtained via the equidistribution of a monitor function. The numerical scheme consists of the implicit Euler scheme for the time derivative and the classical central difference scheme for the spatial derivative. A truncation error analysis and a stability analysis are carried out. It is shown that the method converges uniformly in the discrete supremum norm with an optimal error bound. Error estimates are derived, and numerical examples are presented.

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Key words

singularly perturbed delay parabolic problem, boundary layers, uniform convergence, equidistribution grid, monitor function

AMS subject classifications

65M06, 65M12

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