一类弱非线性常微分方程的插值摄动解法

The Interpolation Perturbation Method for Solving A Class of Weakly Nonlinear Differential Equations

用插值摄动法［１］ 研究一类弱非线性常微分方程的初值问题， 得到了一级及二级近似解． 解的精度很高， 并逐级提高． 如果用正则摄动法求解此类问题， 则当自变量较大时， 误差很大．

In this paper,the authors study the initial value problems of a class of weakly nonlinear differential equation.The first and the second order approximate solutions are obtained.Their accuracies are high and the more the approximate order is high,the more the accuracy is high.If the regular perturbation method is used to solve the same problems,then,when the independent variable is big,so is the error of the solution.