Numerical Performance of Half-Sweep SOR Iteration with the Grünwald Implicit Finite Difference for Time-Fractional Parabolic Equations

Fatihah Anas Muhiddin, Jumat Sulaiman, Andang Sunarto

In this paper, Grünwald implicit difference approximation equations were formulated by discretizing one-dimensional (1D) time-fractional parabolic equations (TFPEs). Then, the linear systems generated were solved using iterative methods. The main aim is to examine the performance of half-sweep concept with Successive Over-Relaxation (HSSOR) method in solving large and sparse linear system that arise from the discretization of the TFPEs. To do that, we also provide the implementation and results of another family of the Successive Over-Relaxation in full-sweep case (FSSOR) iterative method, which will act as a control method for result verification purposes. Three examples were considered to examine the efficiency of the proposed method. From the numerical results, it shows that HSSOR iteration technique is more efficient in regards to the iteration numbers and computation time.

Volume 11 | 12-Special Issue

Pages: 119-125