Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902597 | Applied Numerical Mathematics | 2018 | 30 Pages |
Abstract
This paper is devoted to the numerical solution of the time fractional cable equation and its inverse problem. The time-space spectral Legendre tau method based on the shifted Legendre polynomial and its operational matrices is used to solve the direct problem. Furthermore, we prove that the approximated solution of this method converges to the exact solution. In addition, the inverse problem is formulated by using the Tikhonov regularization, the stability and convergence for the inverse problem are provided, then we analyse the sensitivity coefficients and apply the nonlinear conjugate gradient method to solve the regularized problem. Finally, some numerical results are carried out to support the theoretical claims.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Xiu Yang, Xiaoyun Jiang, Hui Zhang,