A ROBUST NUMERICAL TECHNIQUE FOR SOLVING NON-LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY LAYER


Cakir F., Çakır M., Cakir H. G.

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, vol.37, no.3, pp.939-955, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.4134/ckms.c210261
  • Journal Name: COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Page Numbers: pp.939-955
  • Keywords: Singularly perturbed, VIDE, difference schemes, uniform con-vergence, error estimates, Bakhvalov-Shishkin mesh, BAKHVALOV-SHISHKIN MESH, RUNGE-KUTTA METHODS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we study a first-order non-linear singularly per-turbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with expo-nential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N-1) uniformly convergent, where N is the mesh parameter. The numerical re-sults on a couple of examples are also provided to confirm the theoretical analysis.