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

• Published in: Communications in nonlinear science & numerical simulation Vol. 72; pp. 342 - 359
• Main Authors: Doha, E.H., Abdelkawy, M.A., Amin, A.Z.M., Lopes, António M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 30.06.2019; Elsevier Science Ltd
• Subjects: Algorithms; Boundary conditions; Collocation; Convergence; Differential equations; Differential thermal analysis; Error analysis; Fractional integro-differential equation; Jacobi–Gauss quadrature; Mathematical analysis; Nonlinear equations; Normal distribution; Riemann–Liouville derivative; Spectral collocation method; Fractional integro-differential equation; Spectral collocation method; Riemann–Liouville derivative; Jacobi–Gauss quadrature
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.01.005

•A new shifted Jacobi–Gauss-collocation algorithm is presented.•Different classes of fractional integro-differential equations are addressed.•Error analysis is performed.•Numerical examples are given for illustrating the method advantages. 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.