非线性常微分方程转向点问题的数值解

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基金项目: 国家自然科学基金资助

Numerical Solution of Nonlinear Ordinary Differential Equation for a Turning Point Problem

摘要: 本文利用文[3]的技巧得到了具转向点的非线性常微分方程边值问题的导数估计,再结合文[4]的方法,证明了所构造的差分格式关于小参数ε的一致收敛性.我们给出了数值例子,数值结果与理论分析完全符合.
- 非线性常微分方程 /
- 转向点 /
- 奇异摄动问题 /
- 差分格式 /
- 一致收敛性
Abstract: By using the method in [3], several useful estimations of the derivatives of the solution of the boundary value problem for a nonlinear ordinary differential equation with a turning point are obtained.With the help of the technique in [4], the uniform convergence on the small parameter ε for a difference scheme is proved.At the end of this paper, a numerical example is given.The numerical result coincides with theoretical analysis.
- nonlinear ordinary differential equation /
- turning point /
- singular perturbation problem /
- difference scheme /
- uniform convergence

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