Finite Difference Approximation for Space Fractional Soil Moisture Diffusion Equation and Its Application

Abstract

The purpose of this paper is to develop the space fractional order explicit finite difference scheme for fractional order soil moisture diffusion equation with the initial and boundary conditions. We prove that the solution of the space fractional order finite difference scheme is conditionally stable and the convergence of the scheme is discussed at the length. Also as an application of this scheme, numerical solution for space fractional soil moisture diffusion equation is obtained and it is represented graphically by the software 'Mathematica'.