CAJ | 학술논문

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。
대우일류비선성주기／변계수미분방정，제출기우정세적분법적수치해법，처리비선성주기／변계수미분방정계통적향응문제。기적분책략시：채용정세적분격식처리상계수부분；채용선성삽치격식처리비선성주기／변계수부분，기계승정세적분방법고도준학적특점，우보증족구적정도여교소적계산량。통과수치산례，여이왕소용적미분방정직접수치적분법(여예고-교정합명법)구득적해가이비교표명，대우급정적정도요구，정세적분법경경제유효，역우엄범용우구유비선성주기／변계수미분방정적공정문제중。
A numerical solution based on the precise integration method is presented for the response problems of nonlinear periodic systems. Its integration tactics is that using precise integration algorithm deals with the constant coefficient parts, using the linear interpolation simplifies the nonlinear periodic coefficient/variant coefficient parts, in order to carry forward the characteristics of high precision of precise integration and to strike a balance between the accuracy and the amount of calculation. The numerical properties of this solution are illustrated by comparing the numerical results and efficiency of the numerical integration methods for the ordinary differential equation such as Hamming' s predictor- corrector. It is concluded that the precise integration algorithm is more efficient and economical with respect to the same accuracy, and is practical for the wide range of engineering problems with the nonlinear periodic system.