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, cilt.72, ss.342-359, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.cnsns.2019.01.005
  • Dergi Adı: Communications in Nonlinear Science and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.342-359
  • Anahtar Kelimeler: Fractional integro-differential equation, Jacobi–Gauss quadrature, Riemann–Liouville derivative, Spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

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.