Numerical solution for the time-Fractional Diffusion-wave Equations by using Sinc-Legendre Collocation Method

Abstract

In this paper the numerical solution of fractional diffusion wave equation is proposed. The fractional derivative will be in the Caputo sense. The proposed method will be based on shifted Legendre collocation scheme and sinc function approximation for time and space respectively. The problem is reduced to the problem into a system of algebraic equations after implementing this method. For demonstrating the validity and applicability of the proposed numerical scheme some examples are presented.

Keywords: Fractional diffusion equation, Sinc functions, shifted Legendre  polynomials, Collocation method.