时间分数阶慢扩散方程的纯显-隐交替并行计算方法

he fractional diffusion equations can accurately describe the migration process of anomalous diffusion,which are widely applied in the field of natural science and engineering calculation.This paper proposed a kind of numerical method with parallel nature which were the pure alternative segment explicit-implicit(PASE-I) and implicit-explicit(PASI-E) difference method for the time fractional diffusion equation.It is based on the combination of the explicit scheme,the implicit scheme and the alternating segment technique.Theoretical analyses have shown that the solution of PASE-I(PASI-E) scheme is uniquely solvable.At the same time the stability and convergence of the scheme were proved by the mathematical induction and Fourier method.Numerical experiments verified the theoretical analyses which showed that the convergence rates are temporally (2-α) order and spatially second-order.Meanwhile the PASE-I(PASI-E) scheme has obvious parallel properties because of the higher computational efficiency compared with the implicit scheme.Therefore it is feasible to use the scheme for solving the time fractional diffusion equation.