Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid
Year: 2010
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 1–22
Abstract
Adaptive grid methods are established as valuable computational technique in approximating effectively the solutions of problems with boundary or interior layers. In this paper, we present the analysis of an upwind scheme for singularly perturbed differential-difference equation on a grid which is formed by equidistributing arc-length monitor function. It is shown that the discrete solution obtained converges uniformly with respect to the perturbation parameter. Numerical experiments illustrate in practice the result of convergence proved theoretically.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2009.m8015
Numerical Mathematics: Theory, Methods and Applications, Vol. 3 (2010), Iss. 1 : pp. 1–22
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Singular perturbation problems delay differential equations boundary layer upwind scheme adaptive mesh uniform convergence.