Numerical solution of Volterra integro-differential equation with delay

Volume 20, Issue 3, pp 255--263 http://dx.doi.org/10.22436/jmcs.020.03.08
Publication Date: February 13, 2020 Submission Date: July 28, 2019 Revision Date: December 05, 2019 Accteptance Date: December 09, 2019

Authors

Erkan Cimen - Department of Mathematics, Faculty of Education, Van Yuzuncu Yil University, 65080, Van, Turkey. Sabahattin Yatar - Department of Mathematics, Institute of Pure and Applied Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey.


Abstract

We consider an initial value problem for a linear first-order Volterra delay integro-differential equation. We develop a novel difference scheme for the approximate solution of this problem via a finite difference method. The method is based on the fitted difference scheme on a uniform mesh which is achieved by using the method of integral identities which includes the exponential basis functions and applying to interpolate quadrature formulas that contain the remainder term in integral form. Also, the method is proved to be first-order convergent in the discrete maximum norm. Furthermore, a numerical experiment is performed to verify the theoretical results. Finally, the proposed scheme is compared with the implicit Euler scheme.


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ISRP Style

Erkan Cimen, Sabahattin Yatar, Numerical solution of Volterra integro-differential equation with delay, Journal of Mathematics and Computer Science, 20 (2020), no. 3, 255--263

AMA Style

Cimen Erkan, Yatar Sabahattin, Numerical solution of Volterra integro-differential equation with delay. J Math Comput SCI-JM. (2020); 20(3):255--263

Chicago/Turabian Style

Cimen, Erkan, Yatar, Sabahattin. "Numerical solution of Volterra integro-differential equation with delay." Journal of Mathematics and Computer Science, 20, no. 3 (2020): 255--263


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