| Riesz空间分布阶的分数阶扩散方程的数值模拟 |
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| 引用本文： | 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. DOI: 10.19715/j.jmuzr.2021.02.01 |
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| 作者姓名： | 陈景华 陈雪娟 |
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| 作者单位： | (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) |
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| 基金项目： | 集美大学科研基金项目;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;福建省自然科学基金项目 |
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| 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.
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| 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 |
Numerical Method for the Distributed-Order Riesz Space Fractional Diffusion Equation |
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| CHEN Jinghua,CHEN Xuejuan. Numerical Method for the Distributed-Order Riesz Space Fractional Diffusion Equation[J]. the Editorial Board of Jimei University(Natural Science), 2021, 26(2): 97-103. DOI: 10.19715/j.jmuzr.2021.02.01 |
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| Authors: | CHEN Jinghua CHEN Xuejuan |
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| Affiliation: | (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) |
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| 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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| Keywords: | space distributed order fractional differential equation stability convergence numerical discretization |
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