Riesz空间分数阶对流扩散方程的一种计算有效求解方法  

A Computationally Efficient Solution Method for a Riesz Space Fractional Advection-Dispersion Equation

作　　者：沈淑君[1] 刘发旺[2] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005 [2]昆士兰理工大学数学科学学院,澳大利亚昆士兰布里斯本4001

出　　处：《厦门大学学报（自然科学版）》2008年第1期20-24,共5页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10271098);澳大利亚国家研究基金(LP0348653)资助

摘　　要：Riesz空间分数阶对流扩散方程是从混沌动力系统导出的.继续Ilic,Liu等的工作,我们提出在有界区域内求解Riesz空间分数阶对流-扩散方程的一种新的计算有效方法.即基于这两个Riesz空间分数阶导数的矩阵表示.这个方法的创新在于这个算子的标准离散得到包含具有相同分数次幂的矩阵的一个常微分方程组,并利用计算有效的分数阶行方法求解.同时借助于分数阶导数的谱表示和拉普拉斯变换,导出这个Riesz空间分数阶对流扩散方程的解析解.最后给出了数值例子来证实数值方法的有效性.In this paper,a Riesz space fractional advection-dispersion equation（RSFADE） is considered,which is derived from the kinetics of chaotic dynamics.Following work by Ilic and Liu et al,a new computationally efficient method for solving the RSFADE on a bounded domain is proposed.The method is based on the matrix representation of both the Riesz space fractional operators.The novelty of this method is that a standard discretisation of the operator leads to a system of ordinary differential equations（ODEs） with the matrix raised the same fractional power.Then the ODEs is solved by a computationally efficient fractional method of lines.Using a spectral representation of the fractional derivatives and the Laplace transform,the analysis solution of this equation is also derived.Finally,a numerical example is given to demonstrate that this numerical method is computationally efficient.

关 键 词：Riesz空间分数阶导数 矩阵转换技巧 拉普拉斯变换 对流一扩散方程 行方法 

分 类 号：O241.82[理学—计算数学]