役使原理与一种新的一阶弱非线性常微分方程式的近似求解法

THE SLAVING PRINCIPLE AND A NEW APPROXIMATE METHOD FOR SOLVING THE FIRST QRDER OF THE WEAK NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

本文应用我们不久前提出的役使原理和高级绝热近似的新概念,得到一个新的近似求解下述弱非线性常微分方程式:和的方法和适用的条件。 用计算机求解几个例子,得到与理论相符的结果。

By using the slaving principle that we suggested before and the concept of the higher order adiabatic approximation, we obtain an opproximate method for solving the following weak nonlinear ordinary differential equations.q=N(q) + F(t) andq = -r(t)q+ pf(q) + F(t) ( r >0, r》|β|)(|-rq|》| βf(q)|)As a comparison we have made some examples. We find that our theoretical results are in agreement with the computer simulations.