非线性微分方程渐近解的阶的数值验证

Numerical Verification of the Order of the Asymptotic Solutions of a Nonlinear Differential Equation

利用Lindstedt-Poincare摄动法,首先求得一个来源于广义相对论的非线性微分方程的渐近解。该渐近解不含长期项,这克服了文献[4]的缺陷。其次,一种数值解验证技术用于证实该渐近解对小参数是一致有效的。

A perturbation method, Lindstedt-Poincare method, is used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity. The asymptotic solutions contain no secular term, which overcomes a defect in Khuri＇s paper. A technique of numerical order verification is applied to demonstrate that the asymptotic solutions are uniformly valid for small parameter.