Uniform convergence difference schemes for singularly perturbed mixed boundary problems

Authors:
X. Cai;F. Liu
Affiliations:
Department of Mathematics, Jimei University, Xiamen 361021, China and Department of Mathematics, Xiamen University, Xiamen 361005, China;Department of Mathematics, Xiamen University, Xiamen 361005, China and School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld 4001, Australia
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Year:
2004

Citing 2
Cited 0

A uniformly accurate finite element method for a singular perturbation problem in conservative form

SIAM Journal on Numerical Analysis
A conservative uniformly accurate difference method for a singular perturbation problem in conservation form

SIAM Journal on Numerical Analysis

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Abstract

In this paper, we consider the conservative form of singularly perturbed ordinary differential equations with mixed boundary conditions. A fitted mesh finite difference scheme is constructed for these problems. The scheme is shown to be uniformly convergent with respect to the perturbed parameter. A class of conservative difference schemes with uniform mesh are also considered. These difference schemes are proved to be first-order uniformly convergent. The computed results for both cases are in good agreement with the exact solutions.