Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

AHMED ZAKI MAHAMED AMIN A. Z. M. A., Abdelkawy M., Amin A. K., Lopes A. M., Alluhaybi A. A., Hashim I.

AIMS Mathematics, vol.8, no.9, pp.20871-20891, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 9
  • Publication Date: 2023
  • Doi Number: 10.3934/math.20231063
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.20871-20891
  • Keywords: shifted Legendre polynomials, shifted Legendre-Gauss-Lobatto quadrature, spectral collocation method, system of mixed Volterra-Fredholm integral equations
  • Istanbul Gelisim University Affiliated: Yes

Abstract

Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.