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Numerical Algorithms
Published in: Numerical Algorithms 1/2020

25-11-2019 | Original Paper

Numerical approximation for a class of singularly perturbed delay differential equations with boundary and interior layer(s)

Authors: Pratima Rai, Kapil K. Sharma

Published in: Numerical Algorithms | Issue 1/2020

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Abstract

This paper is devoted to the study of singularly perturbed delay differential equations with or without a turning point. The solution of the considered class of problems may exhibit boundary or interior layer(s) due to the presence of the perturbation parameter, the turning point, and the delay term. Some a priori estimates are derived on the solution and its derivatives. To solve the problem numerically, a finite difference scheme on piecewise uniform Shishkin mesh along with interpolation to tackle the delay term is proposed. The solution is decomposed into regular and singular components to establish parameter uniform error estimate. It is shown that the proposed scheme converges to the solution of the continuous problem uniformly with respect to the singular perturbation parameter. The numerical experiments corroborate the theoretical findings.
previous article On convergence of continuous half-explicit Runge-Kutta methods for a class of delay differential-algebraic equations
next article Accurate computations for eigenvalues of products of Cauchy-polynomial-Vandermonde matrices

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Metadata
Title
Numerical approximation for a class of singularly perturbed delay differential equations with boundary and interior layer(s)
Authors
Pratima Rai
Kapil K. Sharma
Publication date
25-11-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 1/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00815-6

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