A Uniformly Convergent Method on Arbitrary Meshes for a Semilinear Convection-Diffusion Problem with Discontinuous Data
Year: 2008
Author: Igor Boglaev, Sophie Pack
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 1 : pp. 24–39
Abstract
This paper deals with a uniform (in a perturbation parameter) convergent difference scheme for solving a nonlinear singularly perturbed two-point boundary value problem with discontinuous data of a convection-diffusion type. Construction of the difference scheme is based on locally exact schemes or on local Green's functions. Uniform convergence with first order of the proposed difference scheme on arbitrary meshes is proven. A monotone iterative method, which is based on the method of upper and lower solutions, is applied to computing the nonlinear difference scheme. Numerical experiments are presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-IJNAM-795
International Journal of Numerical Analysis and Modeling, Vol. 5 (2008), Iss. 1 : pp. 24–39
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: convection-diffusion problem discontinuous data boundary layer uniform convergence monotone iterative method.