Computational algorithm PAOR for time-fractional diffusion equations

Abstract

We deal with the application of an unconditionally implicit finite difference approximation equation of the one-dimensional linear time fractional diffusion equations (TFDE’s) via the Caputo’s time fractional derivative. Based on this implicit approximation equation, the corresponding linear system can be generated in which its coefficient matrix is large scale and sparse. To speed up the convergence rate in solving the linear system iteratively, we construct the corresponding preconditioned linear system. Then we formulate and implement the Preconditioned AOR (PAOR) iterative method for solving the generated linear system. One example of the problem is presented to illustrate the effectiveness of PAOR method. The numerical results of this study show that the proposed iterative method is superior to PSOR and PGS, GS iterative method.