Improved matrix transform method for the Riesz space fractional reaction dispersion equation

The Riesz space fractional reaction dispersion equation is a generalization of the classical reaction dispersion equation. In this paper, we develop a class of different form difference scheme for solving the Riesz space fractional reaction dispersion equation based on the parameter spline function and improved matrix transform method. Stability of the difference schemes are discussed by the matrix method. Finally, some numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.