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

• Autores: Fevzi Erdogan, Mehmet Giyas Sakar, Onur Saldır
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 5, Nº. 1, 2020, págs. 425-436
• Idioma: inglés
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• Resumen

  • 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.