A Novel Uniform Numerical Approach to Solve a Singularly Perturbed Volterra Integro-Differential Equation

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In this paper, the initial value problem for the second order singularly perturbed Volterra integro-differential equation is considered. To solve this problem, a finite difference scheme is constructed, which based on the method of integral identities using interpolating quadrature rules with remainder terms in integral form. As a result of the error analysis, it is proved that the method is first-order convergent uniformly with respect to the perturbation parameter in the discrete maximum norm. Numerical experiments supporting the theoretical results are also presented.

Sobre autores

M. Cakira

Department of Mathematics, Van Yuzuncu Yil University

Email: cimenerkan@hotmail.com
Van, Turkey

E. Cimena

Department of Mathematics, Van Yuzuncu Yil University

Autor responsável pela correspondência
Email: cimenerkan@hotmail.com
Van, Turkey

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Declaração de direitos autorais © M. Cakira, E. Cimena, 2023