基于常微分方程边值问题的Chebyshev谱方法  

Chebyshev Spectral Method In Solving the Boundary Value Problems of the Ordinary Differential Equation

作　　者：易洲[1] 张丽丽[1] 李华[1] 

机构地区：[1]暨南大学物理系,广东广州510632

出　　处：《数学的实践与认识》2015年第16期300-306,共7页Mathematics in Practice and Theory

摘　　要：常微分方程边值问题的数值解法有多种,其中较常用的是化边值问题为初值问题解法以及边值问题差分解法.常微分方程边值问题数值解的Chebyshev谱方法是近年来出现的一种新解法.作为应用例子,分别采用Chebyshev谱方法、化边值问题为初值问题解法、以及边值问题差分解法对一类二阶常微分方程边值问题进行数值求解,并对数值解的精确性及计算时间定量地比较,从而说明Chebyshev解法是精度很高的一种快捷解法.There are several numerical methods to solve the boundary value problems（BVP） of ordinary differential equation（ODE）, among which the method of transferring BVPs to initial vahm problems（IVP） and the differential method of BVPs are the most frequently used. Chebyshev spectral method is a novel approach recently. As an example of applica- tion, to numerically solve a kind of second order BVPs of the ODE in Matlab, we adopted Chebyshev spectral method, the method of transferring BVPs to IVPs and differential meth- ods of BVPs, respectively. Furthermore, we quantitively compared the accuracy of solutions and the time of calculation. Our results show that Chebyshev spectral method is a highly accurate numerical method, as well as a good convenience method.

关 键 词：Chebyshev谱方法 常微分方程 边值问题 

分 类 号：O175.8[理学—数学]