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Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid

Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid
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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.

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