[1]陈景华,陈雪娟.Riesz空间分布阶的分数阶扩散方程的数值模拟[J].集美大学学报(自然科学版),2021,26(2):97-103.
　CHEN Jinghua,CHEN Xuejuan.Numerical Method for the Distributed-Order Riesz Space Fractional Diffusion Equation[J].Journal of Jimei University,2021,26(2):97-103.
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Riesz空间分布阶的分数阶扩散方程的数值模拟(PDF)

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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

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

作者:: 陈景华1; 2; 陈雪娟1; 2; (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)

Author(s):: CHEN Jinghua1; 2; CHEN Xuejuan1; 2; (1.School of Science,Jimei University,Xiamen 361021,China;2.Digital Fujian Big Data Modeling and Intelligent Computing Institute,School of Science,Jimei University,Xiamen 361021,China)

Keywords:: space distributedorder; fractional differential equation; stability; convergence; numerical discretization

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。

Abstract:: 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.

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[2]叶星旸.基于分数阶微分方程的木马病毒传播规律[J].集美大学学报(自然科学版),2019,24(2):145.
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更新日期/Last Update: 2021-05-17