Jacobi Collocation Approximation for Solving Multi-dimensional Volterra Integral Equations

Abdelkawy M. A., Amin A. Z. M. A., Bhrawy A. H., Tenreiro MacHado J. A., Lopes A. M.

International Journal of Nonlinear Sciences and Numerical Simulation, vol.18, no.5, pp.411-425, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1515/ijnsns-2016-0160
  • Journal Name: International Journal of Nonlinear Sciences and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.411-425
  • Keywords: error analysis, shifted Jacobi polynomials, spectral collocation method, system of Volterra integral equation, Volterra integral equation
  • Istanbul Gelisim University Affiliated: No

Abstract

This paper addresses the solution of one- and two-dimensional Volterra integral equations (VIEs) by means of the spectral collocation method. The novel technique takes advantage of the properties of shifted Jacobi polynomials and is applied for solving multi-dimensional VIEs. Several numerical examples demonstrate the efficiency of the method and an error analysis verifies the correctness and feasibility of the proposed method when solving VIE.