Efficient numerical algorithm for spatiotemporal fractional diffusion equation
This paper studies the efficient numerical algorithms for spatiotemporal fractional diffusion equations,in which Caputo type fractional derivatives are used in time and Riemann-Liouville type fractional derivatives are used in space.Firstly,a uniformly convergent high-order numerical discretization scheme is used in time,and the shifted Grünwald-Letnikov formula is used in space for discretization.Secondly,the coefficient matrix structure of the dis-cretized algebraic equations is analyzed,and a fast computing method for solving the spatiotemporal fractional order is established by using fast Fourier transform and GMRES iterative method.Finally,the numerical results show that the numerical scheme is effective.
万方数据
维普
