求解非线性动力学方程的错差迭代法  

Cross iterative algorithm for solving nonlinear dynamical equations

作　　者：张小杭[1,2] 樊社新[1] 袁军[1] 秦宇[1] 

机构地区：[1]广西大学机械工程学院,南宁530004 [2]福建中烟工业公司龙岩烟草工业有限责任公司,龙岩364000

出　　处：《机械设计与制造》2009年第11期219-221,共3页Machinery Design & Manufacture

基　　金：广西制造系统与先进制造技术重点实验室科研项目(07109008_001_Z);广西研究生教育创新计划资助项目(2008105931202M55)

摘　　要：针对如何求解非线性动力学方程提出了一种错差迭代方法。首先待求系统须能表示成由线性齐次部分与非线性部分组成的一阶微分方程组的形式,然后以方程组所对应线性齐次系统的解析解作为初始解,代入一阶微分方程组的非线性部分,组成新的非齐次线性方程组,并求其解析解。以此解析解替代初始解,重复上述迭代过程以求得满足要求的系统近似解。最后利用谐波函数或多项式函数对解进行数据拟合,得到形式简单易用的近似解。算例表明该算法的有效性和实用性。A new cross iterative algorithm base on value range was proposed in a creative way. First of all,the nonlinear dynamical system was transformed to the form of first -order differential equations which include the linear and nonlinear parts. Then being the initial solutions,the analytical solutions which corresponding to homogeneous differential equations were substituted into the nonlinear part of the first-order differential equations to built the new linear equations and a new solutions was solved by them.Then repeat the iterative method until the solutions meets accuracy requirements. At last a data fitting of oS the solutions was made by using the harmonic or polynomial function. The efficiency and applicability this estimate technique are demonstrated by simulation results.

关 键 词：非线性动力学系统 值域 错差迭代法 数据拟合 

分 类 号：TH16[机械工程—机械制造及自动化] O175.14[理学—数学]