An Efficient Numerical Method for Solving the Fractional Diffusion Equation

摘要

Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bioengineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional diffusion equation (FDE) is considered. The fractional derivative is described in the Caputo sense. The method is based upon Legendre approximations. The properties of Legendre polynomials are utilized to reduce FDE to a system of ordinary differential equations, which solved by the finite difference method. Numerical solutions of FDE are presented and the results are compared with the exact solution.