一类带变系数的空间分数阶偏微分方程的Chebyshev拟谱分法（英文）  

Chebyshev Pseudo-spectral Method for a Class of Space Fractional Partial Differential Equations with Variable Coefficients

作　　者：杨银[1] 

机构地区：[1]湘潭大学土木工程与力学学院、科学工程计算与数值仿真湖南省重点实验室,湘潭 411105

出　　处：《工程数学学报》2014年第5期745-752,共8页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11301446);the Postdoctoral Science Foundation of China(2013M531789);the Scientific Research Fund of Hunan Provincial Science and Technology Department(2013RS4057);the Research Foundation of Hunan Provincial Education Department(13B116)

摘　　要：分数阶微分方程已经广泛地应用于工程等各个领域.在本文中,我们针对一类带变系数的空间分数阶偏微分方程,提出了一种Chebyshev拟谱的数值方法,其中分数阶导数是由Caputo分数阶导数定义.该方法能将空间分数阶偏微分方程转化为一个常微分方程,然后在时间上用有限差分方法离散.数值实验表明该方法是有效的.Fractional partial differential equations （FPDEs） have recently been applied in var-ious areas of engineering, science, finance, applied mathematics, bioengineering and others. In this paper, an efficient numerical method for solving a class of space fractional partial differential equations （SFPDEs） with variable coefficients is con-sidered. The fractional derivative is described in the Caputo sense. The method is based upon Chebyshev approximations. The properties of Chebyshev polynomi-als are utilized to reduce SFPDEs to a system of ordinary differential equations, which is solved by the finite difference method. Numerical solutions of SFPDEs are presented and the results are compared with the exact solution.

关 键 词：空间分数阶偏微分方程 CHEBYSHEV多项式 拟谱方法 CAPUTO导数 

分 类 号：O1-8[理学—数学]