Spectral method for time-space fractional partial differential equation
The diffusion equation is one of the fundamental equations in physics.This paper investigates the numerical solution of spectral method for a time-space fractional diffusion equation.In the article,the temporal semi-discrete scheme is constructed using the LI interpolation approximation scheme of the Caputo fractional order.The existence of uniqueness and stability of the solution in this semi-discrete scheme is demonstrated,and the error analysis of the semi-discrete scheme is rigorously discussed.On the basis of this semi-discrete scheme,the fully discrete scheme is obtained by discretizing it in the spatial direction using the Legendre spec-tral method.It is further shown that the solution of this fully discrete scheme exists,is unique,and unconditionally stable.Conclu-sions on the error between the numerical and exact solutions is given and rigorously discussed in the article.
time-space fractional diffusion equationsspectral methodexistence and uniqueness of solutionsstabilityerror ansalysis
万方数据
维普
