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A second-order difference scheme for a parameterized singular perturbation problem

✍ Scribed by Zhongdi Cen

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
250 KB
Volume
221
Category
Article
ISSN
0377-0427

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✦ Synopsis

In this paper we consider a singularly perturbed quasilinear boundary value problem depending on a parameter. The problem is discretized using a hybrid difference scheme on Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independent of singular perturbation parameter. Numerical experiments support these theoretical results.

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## Abstract We generate an exponential splines difference scheme for a one‐dimensional singularly perturbed selfadjoint problem along with general boundary conditions of the third kind. We obtain \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm O(h min(}h,\sqrt \varepsilon)) $\end{doc