A Finite Point Method for Solving the Time Fractional Richards’ Equation

Abstract

In this paper, we propose a numerical method for solving the time fractional Richards’ equation. We first approximate the time fractional derivative of the mentioned equations by a scheme of order O(τ2−α), 0 < a<1; then, we use the finite point method to approximate the spatial derivatives. Before the discrete spatial derivatives, we introduced the basic principles of the finite point method. We solve the one- and two-dimensional versions of these equations using the proposed method. Moreover, the stability properties of the discretized scheme related to time are theoretically analyzed. Numerical results showed the efficiency of the method presented in this paper.