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对于一类非线性周期/变系数微分方程,提出基于精细积分法的数值解法,处理非线性周期/变系数微分方程系统的响应问题。其积分策略是:采用精细积分格式处理常系数部分;采用线性插值格式处理非线性周期/变系数部分,既继承精细积分方法高度准确的特点,又保证足够的精度与较小的计算量。通过数值算例,与以往所用的微分方程直接数值积分法(如预估-校正哈明法)求得的解加以比较表明,对于给定的精度要求,精细积分法更经济有效,易于广泛用于具有非线性周期/变系数微分方程的工程问题中。
For a class of nonlinear periodic / variable coefficient differential equations, a numerical solution based on the precise integral method is proposed to deal with the response of nonlinear periodic / variable coefficient differential equations. The integral strategy is to process the constant coefficient part by using the fine integral format, and to deal with the nonlinear periodic / variable coefficient part by using the linear interpolation format, which not only inherits the highly accurate characteristic of the fine integral method but also ensures enough precision and smaller calculation amount. Numerical examples are compared with the solutions obtained by the direct numerical integration (such as estimated-corrected Hamming method) of differential equations used in the past, which shows that the precise integral method is more economical and effective and can be widely used for a given accuracy requirement In engineering problems with nonlinear periodic / variable coefficient differential equations.