求解非线性动力学方程的渐近数值方法  

Asymptotic numerical method for nonlinear dynamic equations

作　　者：梅树立[1] 邢如义[2] 张森文[3] 

机构地区：[1]中国农业大学信息与电气工程学院,北京100083 [2]河北科技学院,河北邯郸510632 [3]暨南大学应用力学研究所,广州510632

出　　处：《中国农业大学学报》2004年第4期92-96,共5页Journal of China Agricultural University

基　　金：国家自然科学基金资助项目 ( 10 372 0 36 );广东省自然科学基金资助项目 ( 0 2 1197)

摘　　要：利用精细积分技术对同伦摄动方法进行了改进 ,构造了一种求解非线性动力学方程的新的渐近数值方法。数值算例结果表明 ,该方法的计算精度高于简单的同伦摄动方法 ,同经典的精细积分法相比 ,该方法计算量小 ,对时间步长不敏感 。A new asymptotic numerical method for nonlinear dynamic equations was proposed. In this method, the homotopy perturbation method was improved by using the precise integration technique. The result of numerical example showed that the new method was more accurate than the simple homotopy perturbation method. And the computational complexity was less than the traditional precise integration method. Furthermore, this method was not sensitive to the time step. It was thus suitable for solving nonlinear equations.

关 键 词：同伦摄动法 精细积分技术 非线性方程 

分 类 号：O241.4[理学—计算数学]