Numerical solution of Volterra integro-differential equation with delay


Çimen E. , Yatar S.

JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, cilt.20, ss.255-263, 2020 (ESCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 20 Konu: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.22436/jmcs.020.03.08
  • Dergi Adı: JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
  • Sayfa Sayıları: ss.255-263

Özet

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.