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 - <p style="text-align: justify;">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.</p>