Volume 38, Issue 6
Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations

Jafar Biazar & Khadijeh Sadri

J. Comp. Math., 38 (2020), pp. 879-902.

Published online: 2020-06

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35R11, 65M15, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

biazar@guilan.ac.ir (Jafar Biazar)

kh.sadri@uma.ac.ir (Khadijeh Sadri)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-879, author = {Biazar , Jafar and Sadri , Khadijeh }, title = {Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1906-m2018-0131}, url = {http://global-sci.org/intro/article_detail/jcm/16972.html} }
TY - JOUR T1 - Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations AU - Biazar , Jafar AU - Sadri , Khadijeh JO - Journal of Computational Mathematics VL - 6 SP - 879 EP - 902 PY - 2020 DA - 2020/06 SN - 38 DO - http://doi.org/10.4208/jcm.1906-m2018-0131 UR - https://global-sci.org/intro/article_detail/jcm/16972.html KW - Fractional partial differential equation, Two-variable Jacobi polynomials, Caputo derivative, Error bound. AB -

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.

Jafar Biazar & Khadijeh Sadri. (2020). Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations. Journal of Computational Mathematics. 38 (6). 879-902. doi:10.4208/jcm.1906-m2018-0131
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