时间分数阶反应-扩散方程混合差分格式的并行计算方法

分数阶反应-扩散方程有深刻的物理和工程背景,其数值方法的研究具有重要的科学意义和应用价值.文中提出时间分数阶反应-扩散方程混合差分格式的并行计算方法,构造了一类交替分段显-隐格式(alternative segment explicit-implicit,ASE-I)和交替分段隐-显格式(alternative segment implicit-explicit,ASI-E),这类并行差分格式是基于Saul’yev非对称格式与古典显式差分格式和古典隐式差分格式的有效组合.理论分析格式解的存在唯一性,无条件稳定性和收敛性.数值试验验证了理论分析,表明ASE-I格式和ASI-E格式具有理想的计算精度和明显的并行计算性质,证实了这类并行差分方法求解时间分数阶反应-扩散方程是有效的.

Parallel computation method of mixed difference schemes for time fractional reaction-diffusion equation

The fractional reaction-diffusion equation has profound physical and engineering background,and its numerical methods are of great scientific significance and application value.A parallel computation method of mixed difference schemes for time fractional reaction-diffusion equation is proposed,and 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.Theoretical analysis shows that the solution of ASE-I(ASI-E)scheme is uniquely solvable,unconditionally stable and convergent.Numerical experiments verify the theoretical analysis,which shows that the ASE-I scheme and the ASI-E scheme have ideal calculation accuracy and obvious parallel computing properties.It is proved that this kind of parallel difference method is effective for solving the time fractional reaction-diffusion equation.