基于等效小参数法的高阶非线性自治系统周期解的计算

The computation of periodic solutions for the high order nonlinear autonomous systems based on the equivalent parameter method

基于等效小参数法基本思想 ,应用分解法原理 ,通过引入逆算符和选择合适的线性与非线性算子 ,提出了一类高阶非线性自治系统周期解的逆算符表达的递推算法 ,并利用Mathematica计算机代数语言开发出相应的软件系统 ,实现了该算法的计算机自动求解 .文中给出了计算实例 ,并将本文算法所得结果与四阶龙格 库塔 (Runge Kutta)数值方法的计算结果作了比较 .实际计算结果表明 ,该算法具有较高的计算精度和较大的普适性 。

Based on the principle of the equivalent para meter method and applying the decomposition method, the inverse operator expression of the periodic solut ions of some type high order nonlinear autonomous systems has been given by intr oducing the athwart factor and selecting the appropriate linear and nonlinear fa ctors. The automatic calculation of this arithmetic has been realized by compute r program in Mathematica language. The examples of practical calculation have al so been presented and the calculation results by this method are compared with t hose from the Runge-Kutta method. And the calculation results show that this ap p roach has the advantages of high accuracy and wide application, so it is an effe ctive tool to calculate the periodic solutions to some type of nonlinear autonom ous systems.