平均化方法的机器实现

Automatical solutions of the averaging methods

应用Mathematica系统的强大的符号运算功能以及该系统提供的控制语句 ,对一类弱非线性系统櫣 +ω20 u =εf(u ,u·)的有效渐近展开式解进行了研究 ,用Mathematica系统实现了一种有效的奇异摄动方法———平均化方法的自动求解问题 ,并通过调试程序做成了程序包。

Some solutions of effectively asymptotic expansions are studied in this paper which would use powerful symbolic operation and control sentence provided by Mathematica system to a weakly nonlinear system ü+ω 2 0u=εf(u, u ·),and some of automatically solving problems of the averaging method are considered such as method of effectively singular pertubations. On the other hand, we have compiled these programs and integrated into packages.