中国空间科学技术

中国空间科学技术

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一般非线性边值问题的高精度方法

周保民   

  1. 北京卫星信息工程研究所
  • 发布日期:1992-10-25

A METHOD OF HIGHER ORDER ACCURAY FOR GENERAL NONLINEAR BOUNDARY VALUE PROBLEMS

Zhou Baomin (Beijing Institute of Satellite Information Engineering)   

  • Online:1992-10-25

摘要： 介绍了满足边界条件y(a)=A 和y(b)=B 的一般二阶非线性常微分方程y″=f(x,y,y′)的六阶三对角有限差分法;在右端项一般形式下,推广了文献[2]的结果。并在适当条件下证明了该方法的收敛性和稳定性,同时用数值试验证实了上述结论的正确性。

关键词: 边值问题, 有限差分理论, 常微分方程, 方法

Abstract: We present a sixth-order finite difference method for the gener- al second-order nonlinear differential equation y″=f(x,y,y′)subject to the boundary conditions y(a)=A,y(b)=B.We establish,under appropriate con- ditions,0(h~6)-convergence of the finite difference scheme.Numerical exam- ples are given to illustrate the method and its sixth-order convergence.

Key words: Boundary value problem, Finite difference theory, Ordinary differential equation, Method