摘要
The fractional diffusion equations can accurately describe the migration process of anomalous diffusion, which are widely applied in the field of natural science and engineering calculations. This paper proposed a kind of numerical methods with parallel nature which were the alternating segment explicit-implicit (ASE-I) and implicit-explicit (ASI-E) difference method for the time fractional sub-diffusion equation. It is based on the combination of the explicit scheme, implicit scheme, improved Saul’yev asymmetric scheme and the alternating segment technique. Theoretical analyses have shown that the solution of ASE-I (ASI-E) scheme is uniquely solvable. At the same time the stability and convergence of the two schemes were proved by the mathematical induction. The theoretical analyses are verified by numerical experiments. Meanwhile the ASE-I (ASI-E) scheme has the higher computational efficiency compared with the implicit scheme. Therefore it is feasible to use the parallel difference schemes for solving the time fractional diffusion equation.
The fractional diffusion equations can accurately describe the migration process of anomalous diffusion, which are widely applied in the field of natural science and engineering calculations. This paper proposed a kind of numerical methods with parallel nature which were the alternating segment explicit-implicit (ASE-I) and implicit-explicit (ASI-E) difference method for the time fractional sub-diffusion equation. It is based on the combination of the explicit scheme, implicit scheme, improved Saul’yev asymmetric scheme and the alternating segment technique. Theoretical analyses have shown that the solution of ASE-I (ASI-E) scheme is uniquely solvable. At the same time the stability and convergence of the two schemes were proved by the mathematical induction. The theoretical analyses are verified by numerical experiments. Meanwhile the ASE-I (ASI-E) scheme has the higher computational efficiency compared with the implicit scheme. Therefore it is feasible to use the parallel difference schemes for solving the time fractional diffusion equation.
