一种与长期项无关的用于求解系统近似解析解的自由迭代法(SFIA)  

A secular-term free iterative algorithm (SFIA) for the approximate analytical solution of nonlinear systems

作　　者：张琬 施三支[1] 吴东旭 ZHANG Wan;SHI San-zhi;WU Dong-xu(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022,China)

机构地区：[1]长春理工大学数学与统计学院,吉林长春130022

出　　处：《东北师大学报（自然科学版）》2022年第3期37-43,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11372117)。

摘　　要：提出了一种新的自由迭代算法(SFIA).根据常数在求解常微分方程时的变化,构造了一个求解非线性系统逼近的迭代过程,无需额外的努力来消除长期项.基于压缩映象原理,给出了SFIA方法收敛性的证明,并特别注意了如何得到一些物理系统的近似解析解,最后给出了实例.A newly developed secular-term free iterative algorithm(SFIA) is proposed.According to the variation of constant in solving ordinary differential equations, we construct an iterative procedure for obtaining the approximation of nonlinear systems, which no need to pay extra efforts to eliminate the secular change terms.A simple proof for the convergence of the finite element method is then given and special attentions are paid how to obtain the approximate analytical solution for some mechanical and physical systems.

关 键 词：长期项 近似解析解 常数变易法 

分 类 号：O224[理学—运筹学与控制论]