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

•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...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2019-06, Vol.72, p.342-359
Main Authors: Doha, E.H., Abdelkawy, M.A., Amin, A.Z.M., Lopes, António M.
Format: Article
Language:English
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
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Summary:•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.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2019.01.005