Parallel Computation Methods For Two Types Of Evolution Equations In Fractional Statistical Dynamics

The fractional evolution equation has a profound physical and engineering background.With the continuous application of the fractional evolution equation,how to solve it quickly has become a very important research topic.Firstly,for time fractional reaction-diffusion equation,a class of alternative segment explicit-implicit scheme(ASE-I)and alternative segment implicit-explicit scheme(ASI-E)are constructed.This kind of parallel difference scheme is based on the effective combination of the Saul'yev asymmetric scheme,classical explicit difference scheme and classical implicit difference scheme.This kind of parallel difference method is analyzed and proved that it is feasible and effective to solve the time fractional reaction-diffusion equation in this paper.Secondly,for time fractional reaction-diffusion equation,a class of improved alternating segment Crank-Nicolson(IASC-N)scheme is constructed.Firstly,it proves theoretically that the IASC-N scheme satisfies our needs for various properties such as stability and convergence.Secondly,selecting specific numerical experiment also further demonstrates that the IASC-N scheme has 2 order spatial precision and 2-? order time precision,and the computational efficiency is greatly improved compared with the implicit scheme and C-N scheme.Lastly,for two-dimensional time fractional convection-diffusion equation,based on the exploration of the parallelization of the traditional difference schemes,a parallel computing method of alternating band Crank-Nicolson(ABdC-N)difference scheme is proposed in this paper.It is a type of parallel difference scheme constructed by combining classical Crank-Nicolson(C-N)scheme with classical explicit and implicit schemes based on the alternating band technique.The numerical experiments verify the theoretical analysis and show that the ABdC-N parallel scheme is much more efficient than the serial classical implicit difference scheme,which reflects the obvious efficiency of the ABdC-N parallel difference scheme for solving two-dimensional time fractional convection-diffusion equation.