半无界非线性热传导方程的Laguerre拟谱方法  

Laguerre pseudospectral method for nonlinear heat transfer equation on semi-infinite interval

作　　者：王天军[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：《应用数学与计算数学学报》2013年第1期9-15,共7页Communication on Applied Mathematics and Computation

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

摘　　要：以Laguerre-Gauss-Radau节点为配置点,利用拟谱方法求数值解,逼近半无界非线性热传导方程非齐次Neumann边界条件的正确解.给出算法格式和相应的数值例子,表明所提算法格式的有效性和高精度.这里所用方法也可用于求解其他非线性问题.This paper deals with the numerical solutions of the nonlinear heat transfer equation with inhomogeneous Neumann boundary conditions on a semi- infinite interval. Laguerre-Gauss-Radua nodes are used to construct the Nth- degree Lagrange interpolation function that approximates the solution to the non- linear heat transfer equation on a semi-infinite interval. Efficient algorithms are implemented. Numerical results demonstrate efficiency and high accuracy of this approach. Especially, it is much easier to deal with the nonlinear heat transfer on a semi-infinite interval. The proposed method is also applicable to other nonlinear problems defined on certain unbounded domains.

关 键 词：非线性热传导方程 非齐次Neumann边界条件 Laguerre拟谱方法 Laguerre-Gauss—Radau节点 

分 类 号：O175.2[理学—数学]