Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6932104 | Journal of Computational Physics | 2015 | 33 Pages |
Abstract
In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and Ï. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
A.H. Bhrawy, M.A. Zaky,