Numerical solution of Volterra integro-differential equation with delay

Volume 20, Issue 3, pp 255--263
Publication Date: February 13, 2020 Submission Date: July 28, 2019 Revision Date: December 05, 2019 Accteptance Date: December 09, 2019


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.


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.