A Novel Uniform Numerical Approach to Solve a Singularly Perturbed Volterra Integro-Differential Equation
- Authors: Cakira M.1, Cimena E.1
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Affiliations:
- Department of Mathematics, Van Yuzuncu Yil University
- Issue: Vol 63, No 10 (2023)
- Pages: 1616-1616
- Section: ОБЫКНОВЕННЫЕ ДИФФЕРЕНЦИАЛЬНЫЕ УРАВНЕНИЯ
- URL: https://journals.rcsi.science/0044-4669/article/view/140287
- DOI: https://doi.org/10.31857/S0044466923100022
- EDN: https://elibrary.ru/EAEXMX
- ID: 140287
Cite item
Abstract
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.
About the authors
M. Cakira
Department of Mathematics, Van Yuzuncu Yil University
Email: cimenerkan@hotmail.com
Van, Turkey
E. Cimena
Department of Mathematics, Van Yuzuncu Yil University
Author for correspondence.
Email: cimenerkan@hotmail.com
Van, Turkey