A New Three-Level Rotated Implicit Method for Solving the Two-Dimensional Time Fractional Diffusion-Wave Equation

Fractional diffusion-wave equation represents many physical phenomena in modeling diffusive processes, waves in fluid flow, and oil strata among others. The numerical solution of this equation is an important task and has been investigated extensively over the last several years. The main purpose of this paper is to formulate a new three time level method in solving the two dimensional time-fractional diffusion-wave equation based on a rotated finite difference approximation formula where the time fractional derivative is described by Caputo's derivative of order 1 < alpha < 2. The developed scheme is derived from the standard implicit formula rotated 45 degrees clockwise with respect to the standard mesh. Numerical example and comparison with the standard classical iterative method has been conducted in this study to test the effectiveness of the proposed method. We show that the proposed iterative method is superior to the standard iterative method in terms of iteration numbers and execution timings without having to jeopardize the accuracy of the solutions.