A note on a parameterized singular perturbation problem

Authors:
G. M. Amiraliyev;Hakki Duru
Affiliations:
Department of Mathematics, Faculty of Art and Sciences, Yüzüncü Yil University, Van 65080, Turkey;Department of Mathematics, Faculty of Art and Sciences, Yüzüncü Yil University, Van 65080, Turkey
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

We consider a Uniform finite difference method on Shishkin mesh for a quasilinear first-order singularly perturbed boundary value problem (BVP) depending on a parameter. We prove that the method is first-order convergent except for a logarithmic factor in the discrete maximum norm, independently of the perturbation parameter. Numerical experiments support these theoretical results.