非线性Fokker-Planck方程的Hermite谱配置方法  

Hermite Spectral Collocation Method for Nonlinear Fokker-Planck Equation

作　　者：王天军[1] 杨森[1] 

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《安徽工业大学学报（自然科学版）》2012年第4期381-384,共4页Journal of Anhui University of Technology（Natural Science）

基　　金：国家自然科学基金项目(11171227);河南省教育厅自然科学基金项目(2011B110014);河南科技大学博士启动基金项目(09001263)

摘　　要：以Hermite-Gauss节点为配置点,用谱配置方法求数值解,逼近无界区域上的非线性Fokker-Planck方程初值问题的理论解。给出算法格式,数值运算表明所提算法格式的有效性和高精度。所给算法尤其适合于非线性问题,也可用于求解无界区域上非线性常微分方程定解问题。Spectral collocation method is employed to obtain the numerical solutions of initial value problem of nonlinear Fokker-Planck equation on unbounded interval, which approximate those of theory solutions, in which Hermitc-Gauss nodes arc used to collocate nodes. Format of algorithm is given and implemented. Numerical results demonstrate its efficiency and high accuracy of this approach. Especially, it is much easier to deal with nonlinear Fokker-Planck equation. The proposed method is also applicable to nonlinear ordinary differential equations defined on certain unbounded domains.

关 键 词：非线性Fokker-Planck方程 初值问题 谱配置方法 Hermite-Gauss节点 

分 类 号：O175.2[理学—数学]