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Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations

Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations
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Year:    2020

Author:    Jafar Biazar, Khadijeh Sadri

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 6 : pp. 879–902

Abstract

Two-variable Jacobi polynomials, as a two-dimensional basis, are applied to solve a class of temporal fractional partial differential equations. The fractional derivative operators are in the Caputo sense. The operational matrices of the integration of integer and fractional orders are presented. Using these matrices together with the Tau Jacobi method converts the main problem into the corresponding system of algebraic equations. An error bound is obtained in a two-dimensional Jacobi-weighted Sobolev space. Finally, the efficiency of the proposed method is demonstrated by implementing the algorithm to several illustrative examples. Results will be compared with those obtained from some existing methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1906-m2018-0131

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 6 : pp. 879–902

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Fractional partial differential equation Two-variable Jacobi polynomials Caputo derivative Error bound.

Author Details

Jafar Biazar

Khadijeh Sadri

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