Caputo's Implicit Solution of Space-Fractional Diffusion Equations by QSSOR Iteration

In this study, we present the Caputo's implicit finite difference solution for the one-dimensional linear space fractional diffusion equations based on the quarter-sweep Caputo's implicit finite difference approximation equation. To derive the approximation equation, firstly the proposed problem will be discretized by using the Caputo's space fractional derivative and the second-order central difference scheme. Then we can construct a linear system which has been solved by using Quarter-Sweep SOR (QSSOR) iterative method. The numerical results of this iterative method will be compared with other existing SOR methods such as Full-Sweep SOR (FSSOR) and Half-Sweep SOR (HSSOR). Finally it can be concluded that the proposed iterative method is superior compared with the FSSOR and HSSOR methods.