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
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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.
Share and Cite
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
Keywords
- Volterra delay integro-differential equation
- finite difference method
- error estimate
MSC
- 34K28
- 65L10
- 65L20
- 65L70
- 65R20
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