Analysis of Stability and Convergence of Numerical Approximation for the Riesz Fractional Reaction-dispersion Equation

Fractional differential equation has been used to simulate many phenomena in engineering,physics,chemistry and other science.However numerical methods and theoretical analysis of fractional diffusion equations are very difficult tasks.Theoretical analysis is different from classical numerical method.A Riesz fractional reaction-dispersion equation(RFRDE) is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β∈(1,2].Using the relationship between the Riemann-Liouville definition and the Grunwald-Letnikov definition,an explicit numerical approximation is presented.The stability and convergence of the approximation are analyzed.Finally,some numerical examples are given.