Original scientific paper

A collocation method on a Gartland-type mesh for a singularly perturbed reaction-diffusion problem

Goran Radojev orcid.org/0000-0002-0996-6691 ; Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Serbia
Mirjana Brdar orcid.org/0000-0002-6466-9219 ; Faculty of Technology, University of Novi Sad, Novi Sad, Serbia

Abstract

A singularly perturbed reaction-diffusion one-dimension problemis solved numerically by collocation method with quadratic \[C^1\]splines. Using appropriately recursively graded mesh the second order of convergence is obtained in the supremum norm uniformly, up to a logarithmic factor, in the singular perturbation parameter. The aim of this paper is to emphasize the importance of using the recursively graded mesh. The former results obtained by mentioned method on the smoothed Shishkin mesh are improved. Numerical experimentssupport the theoretical results. Numerical results for the reaction-diffusion problem in two-dimension show the same order of the convergence as well as in one-dimensional case, but theoretical analysis presents an ongoing work.

Keywords

Reaction-diffusion problems; collocation; singular perturbation; recursively graded mesh

Hrčak ID:

215148

URI

https://hrcak.srce.hr/215148

Publication date:

19.4.2019.

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