Numerical Methods For Two Classes Of Fractional Diffusion Equations

This paper is mainly divided into two parts. In the first part, the implicit midpoint method is constructed to solve the modified anomalous sub-diffusion equation with a nonlinear source term. The theoretical results about the stability and convergence of the method are obtained. The availability of the numerical method is indicated by numerical experiment. In the second part, the midpoint splitting method is proposed to solve the problem of nonlinear composite stiff ordinary differential equation with initial value. Then the stability, consistency and convergence of this method are proved and the correspondent theoretical results are obtained. Lastly the method is applied to solve two dimension space fractional diffusion equation with initial and boundary value. Numerical experiment further demonstrates the correctness of the theory and also indicates the validity of algorithm.