Riesz空间分布阶的分数阶扩散方程的数值模拟

Numerical Method for the Distributed-Order Riesz Space Fractional Diffusion Equation

提出一种求解Riesz空间分布阶的分数阶扩散方程的数值方法。利用辛普森数值求积公式,将分布阶微分方程离散为一个多项分数阶导数的微分方程;利用四阶差分格式求解此具有多项分数阶导数的微分方程,并运用能量法分析数值格式的稳定性和收敛性。同时,给出数值例子,说明所建立的数值离散格式的有效性。

A numerical method for solving the fractional diffusion equation of the distributed-order Riesz space fractional diffusion equation was proposed.The distributed-order differential equation was discretized into a differential equation with a multi-term equation by Simpson quadrature formula.The fourth-order difference approximation was derived to solve the resulting multi-term equation.The stability and convergence of the numerical scheme were analyzed by energy method,and a numerical example was given to illustrate the validity of the established numerical discrete scheme.