带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

PREDICTOR-CORRECTOR APPROACH FOR RIESZ TEMPERED FRACTIONAL DIFFUSION EQUATION WITH A NONLINEAR SOURCE TERM

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.

In this paper,a new numerical scheme is constructed for solving Riesz tempered fractional diffusion equation with a nonlinear source term in which the predictor-corrector approach is applied to discretize the time partial derivative and the modified second-order Lubich tempered difference operator is used to approximate the Riesz space tempered fractional partial derivative.The stability and convergence analysis of the numerical scheme are given under a certain condition,and there are both second order for the time and space convergence order of this numerical scheme.Numerical experiments demonstrate that the numerical method is effective.