Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay


Yapman Ö., Amiraliyev G. M., Amirali I.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.355, pp.301-309, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 355
  • Publication Date: 2019
  • Doi Number: 10.1016/j.cam.2019.01.026
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.301-309
  • Keywords: Finite difference method, Volterra delay-integro-differential equation, Singular perturbation, Uniform convergence, LINEAR MULTISTEP METHODS, DIFFERENTIAL EQUATIONS, STABILITY ANALYSIS, KERNEL
  • Erzincan Binali Yildirim University Affiliated: Yes

Abstract

In this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra integro-differential equation was considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form, a fitted difference scheme is constructed and analysed. It is shown that the method displays first order uniform convergence in perturbation parameter. Some numerical results are given to confirm the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.