用加权残余法求解含大参数的Duffing方程

Approximate Solution for Duffing Equation with Large Parameter via Method of Weighted Residuals

本文应用加权残余法分析了含大参数的 Duffing方程 ,并得到了整个区域内 (0 <ε<∞ )一致有效的近似解 ,得到的近似周期的最大相对误差小于 7.0 % ,当参数为小量时 (ε 1 ) ,得到的近似解和摄动解完全一致 .

In this paper, the Duffing equation with very large parameter (0< ε <∞) is studied by the weighted residual method. The obtained results are valid not only for small parameter, but also for very large values of the parameter. Even when ε→∞ , the maximal relative error of the periodic is less than 7 0%.