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Numerical Algorithms
Published in: Numerical Algorithms 1/2020

08-06-2019 | Original Paper

A priori error estimates of a Jacobi spectral method for nonlinear systems of fractional boundary value problems and related Volterra-Fredholm integral equations with smooth solutions

Authors: Mahmoud A. Zaky, Ibrahem G. Ameen

Published in: Numerical Algorithms | Issue 1/2020

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Abstract

Our aim in this paper is to develop a Legendre-Jacobi collocation approach for a nonlinear system of two-point boundary value problems with derivative orders at most two on the interval (0,T). The scheme is constructed based on the reduction of the system considered to its equivalent system of Volterra-Fredholm integral equations. The spectral rate of convergence for the proposed method is established in both L2- and \( L^{\infty } \)- norms. The resulting spectral method is capable of achieving spectral accuracy for problems with smooth solutions and a reasonable order of convergence for non-smooth solutions. Moreover, the scheme is easy to implement numerically. The applicability of the method is demonstrated on a variety of problems of varying complexity. To the best of our knowledge, the spectral solution of such a nonlinear system of fractional differential equations and its associated nonlinear system of Volterra-Fredholm integral equations has not yet been studied in literature in detail. This gap in the literature is filled by the present paper.
previous article Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations
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Appendix
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Metadata
Title
A priori error estimates of a Jacobi spectral method for nonlinear systems of fractional boundary value problems and related Volterra-Fredholm integral equations with smooth solutions
Authors
Mahmoud A. Zaky
Ibrahem G. Ameen
Publication date
08-06-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 1/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00743-5

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