Shifted Jacobi–Gauss-collocation with convergence analysis for fractional integro-differential equations

Doha E., Abdelkawy M., Amin A. Z. M. A., Lopes A. M.

Communications in Nonlinear Science and Numerical Simulation, vol.72, pp.342-359, 2019 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 72
  • Publication Date: 2019
  • Doi Number: 10.1016/j.cnsns.2019.01.005
  • Journal Name: Communications in Nonlinear Science and Numerical Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.342-359
  • Keywords: Fractional integro-differential equation, Jacobi–Gauss quadrature, Riemann–Liouville derivative, Spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

A new shifted Jacobi–Gauss-collocation (SJ-G-C) algorithm is presented for solving numerically several classes of fractional integro-differential equations (FI-DEs), namely Volterra, Fredholm and systems of Volterra FI-DEs, subject to initial and nonlocal boundary conditions. The new SJ-G-C method is also extended for calculating the solution of mixed Volterra–Fredholm FI-DEs. The shifted Jacobi–Gauss points are adopted for collocation nodes and the FI-DEs are reduced to systems of algebraic equations. Error analysis is performed and several numerical examples are given for illustrating the advantages of the new algorithm.