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A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

Jha, Anuradha and Kadalbajoo, Mohan K (2015) A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems. In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 92 (6). pp. 1204-1221.

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Official URL: http://dx.doi.org/ 10.1080/00207160.2014.928701

Abstract

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Item Type: Journal Article
Keywords: 65M12; 65M06; uniform convergence; Shishkin-Bakhvalov mesh; upwind method; two parameters; singular perturbations; unsteady problem
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 01 Apr 2015 12:08
Last Modified: 01 Apr 2015 12:08
URI: http://eprints.iisc.ac.in/id/eprint/51123

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