Convergence analysis of the numerical method for a singularly perturbed periodical boundary value problem

Volume 16, Issue 2, pp 248-255 http://dx.doi.org/10.22436/jmcs.016.02.13

Publication Date: June 15, 2016 Submission Date: January 22, 2016

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Authors

Musa Cakir - Department of Mathematics, Faculty of Science, Yuzuncu Yil University, 65080, Van, Turkey. Ilhame Amirali - Department of Mathematics, Faculty of Art and Sciences, Duzce University, 81620, Duzce, Turkey. Mustafa Kudu - Department of Mathematics, Faculty of Art and Sciences, Erzincan University, 24000, Erzincan, Turkey. Gabil M. Amiraliyev - Department of Mathematics, Faculty of Art and Sciences, Erzincan University, 24000, Erzincan, Turkey.

Abstract

This work deals with the singularly perturbed periodical boundary value problem for a quasilinear second-order differential equation. The numerical method is constructed on piecewise uniform Shishkin type mesh, which gives first-order uniform convergence in the discrete maximum norm. Numerical results supporting the theory are presented.

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Keywords

• Singular perturbation
• periodical problem
• fitted difference method
• uniformly convergent
• boundary layer.

MSC

•  65L12
•  65L70
•  34B10
•  34D15

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