Numerical Analysis Of Some Difference Methods For Time Fractional Reaction-Diffusion Equations

The fractional reaction-diffusion equation has profound physical background and theoretical connotation,and its numerical solution is of great scientific significance and practical value.In this dissertation,two kinds of difference methods are proposed for one-dimensional time fractional reaction-diffusion equation.One is the serial difference method:explicit-implicit(E-I)difference method and implicit-explicit(I-E)difference method,which are constructed by the combination of classical explicit scheme and classical implicit scheme.The other is the parallel difference method:pure alternative segment explicit-implicit(PASE-I)difference method and pure alternative segment implicit-explicit(PASE-I)difference method.PASI-E difference method is based on the combination of classical explicit scheme and classical implicit scheme with alternating piecewise technique.In this dissertation,the existence and uniqueness of solutions for two kinds of difference schemes are analyzed.Both theoretical analysis and numerical experiments show that the E-I and I-E difference methods,PASE-I and PASI-E difference methods are unconditionally stable and convergent,with two-order spatial accuracy and 2-a order temporal accuracy.At the same time,the computational efficiency of the two kinds of difference methods is higher than that of classical implicit difference methods.This method is efficient and feasible for solving fractional order reaction-diffusion equation.