Shifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction–diffusion equations

This paper proposes a new method for solving distributed order time-fractional reaction–diffusion equations (DO-TFRDEs). Extended versions of the shifted Jacobi–Gauss–Lobatto and shifted fractional order Jacobi–Gauss–Radau collocation methods are developed for reducing the DO-TFRDEs to systems of al...

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Bibliographic Details
Published in:Computational & applied mathematics Vol. 38; no. 2; pp. 1 - 21
Main Authors: Abdelkawy, M. A., Lopes, António M., Zaky, M. A.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2019
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Collocation methods
Computational mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Reaction-diffusion equations
Distributed order fractional reaction–diffusion equation
65M70
74S25
26A33
Spectral collocation method
35R11
Caputo fractional derivative
ISSN:2238-3603, 1807-0302
Online Access:Get full text
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Summary:This paper proposes a new method for solving distributed order time-fractional reaction–diffusion equations (DO-TFRDEs). Extended versions of the shifted Jacobi–Gauss–Lobatto and shifted fractional order Jacobi–Gauss–Radau collocation methods are developed for reducing the DO-TFRDEs to systems of algebraic equations and computing their approximate solutions. The applicability and accuracy of the method is illustrated through numerical examples.
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ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-019-0845-1