空间分数阶扩散方程的超线性收敛离散格式

Abstract

考虑了空间分数阶扩散方程的数值解,构造了一个隐式差分离散格式,证明了此格式是无条件稳定的,且关于空间步长是超线性收敛的.最后,给出一个数值例子说明本文的理论分析是正确的,所构造的离散格式是有效的.

The space fractional order diffusion equation is considered.A implicit difference scheme is constructed,which is unconditionally stable and convergent.The convergent order is superlinear about space step.Finally,one example is presented to show that the numerical analysis is right and the method is feasible and efficient.