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

作　　者：陈景华[1,2] 陈雪娟[1,2] CHEN Jinghua;CHEN Xuejuan(School of Science,Jimei University,Xiamen 361021,China;Digital Fujian Big Data Modeling andIntelligent Computing Institute,School of Science,Jimei University,Xiamen 361021,China)

机构地区：[1]集美大学理学院,福建厦门361021 [2]集美大学理学院数字福建大数据建模与智能计算研究所,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2021年第2期97-103,共7页Journal of Jimei University：Natural Science

基　　金：福建省自然科学基金项目(2019J01329,2020J01703);集美大学科研基金项目(ZP2020054);集美大学数字福建大数据建模与智能计算研究所开放基金。

摘　　要：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.

关 键 词：空间分布阶 分数阶微分方程 稳定性 收敛性 数值离散 

分 类 号：O241.82[理学—计算数学]