<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.</p></abstract>

The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.

A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

Department of Mathematics, Faculty of Science

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

The purpose of this paper is to present a uniform finite difference method for numerical solution of a initial value problem for semilinear second order...

A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

Publié en ligne: 31 mars 2020

Pages: 425 - 436

Reçu: 11 juin 2019

Accepté: 13 août 2019

DOI: https://doi.org/10.2478/amns.2020.1.00040

Mots clés
Delay differential equation, Singular perturbation, Finite difference scheme, Piecewise-uniform mesh, Error estimates

© 2019 Fevzi Erdogan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations

Publié en ligne: 31 mars 2020

Pages: 425 - 436

Reçu: 11 juin 2019

Accepté: 13 août 2019

DOI: https://doi.org/10.2478/amns.2020.1.00040

Mots clésDelay differential equation, Singular perturbation, Finite difference scheme, Piecewise-uniform mesh, Error estimates

© 2019 Fevzi Erdogan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Delay differential equation, Singular perturbation, Finite difference scheme, Piecewise-uniform mesh, Error estimates