The Quasi-compact Finite Difference Schemes For Time-space Fractional Diffusion Equation

This article is mainly divided into two parts.In the first part,we study the finite difference method for the initial–boundary problem of one dimensional time-space fractional diffusion equation.The Caputo temporal fractional derivative is approximated by L1-2interpolation method,and the Riemann-Liouville fractional derivative is discretized by quasicompact difference operator,thus a class of new compact difference algorithm is constructed.The stability and convergence of the proposed numerical method is proved by energy method.Numerical results verify that the proposed numerical method is effective.In the second part,based on the study of the one dimensional problem,a new altering direction implicit scheme is constructed for solving the initial–boundary problem of two dimensional timespace fractional diffusion equation.The theoretical result of stability and convergence are discussed by energy method.Numerical result demonstrate that the proposed numerical method is effective.