求解非线性问题的一种方法

A Method for Seeking the Solutions of Non-linear Problems

提出一个求解强非线性问题的新方法．此法不要求微分方程中含有微量项，只是将预估的零级近似解加以修正，使之逐渐逼近于真实解，可把一个非线性问题转化成为一个线性问题。算例表明，对求解强非线性问题比已有的正则或奇异摄动解法更有效．

In this paper, the author proposes a new method for seeking the solution of nonlinear problems.This method does not demand that in the differenctial equations have the terms of small quantities. We onlyprogressively correct the prejudged zeroth approximate solution in order that it progressively approaches theexact solution.The new method transforms the nonlinear problem into a linear one. There are calculationexamples. Calculation examples show that for seeking to solve the nonlinear problems the method is bet- ter than the known regular or singular pertubation methods.