Abstract
In this paper, we construct a class of semi-implicit difference method for time fractional diffusion equations—the group explicit (GE) difference scheme, which is a difference scheme with good parallelism constructed using Saul’yev asymmetric scheme. The stability and convergence of the GE scheme of time fractional diffusion equation are analyzed by mathematical induction. Then, the theoretical analysis is verified by numerical experiments, which shows that the GE scheme is effective for solving the time fractional diffusion equation.
Highlights
The fractional anomalous diffusion model has a profound physical background and rich theoretical connotation
We construct a class of semi-implicit difference method for time fractional diffusion equations—the group explicit (GE) difference scheme, which is a difference scheme with good parallelism constructed using Saul’yev asymmetric scheme
The theoretical analysis is verified by numerical experiments, which shows that the GE scheme is effective for solving the time fractional diffusion equation
Summary
The fractional anomalous diffusion model has a profound physical background and rich theoretical connotation. We mainly study the fast numerical algorithm of fractional differential equation to improve the numerical simulation efficiency of fractional order modeling this paper. Zhang and Gu [19] proposed a piecewise implicit scheme for the integer order diffusion equations in an asymmetrical scheme, and used alternating techniques to construct multiple explicitimplicit and implicit alternating parallel methods. Gong and Bao [20] [21] performed parallel computation on the explicit difference schemes of fractional reaction-diffusion equations. We do not study the parallel algorithm of equations from the perspective of numerical algebra, but based on the parallelization of traditional differential schemes for solving fractional diffusion equations numerically [23]. The theoretical analysis is verified by numerical experiments, which shows that the GE scheme is very effective for solving time fractional diffusion equations
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