中山大学学报（自然科学版）Issue(4)：8-12,22,6.DOI:10.13471/j.cnki.acta.snus.2015.04.002
一种基于加权残值法的高阶辛算法
A High Order Symplectic Algorithm Based on Weighted Residual Method
摘要
Abstract
A new way to construct high order symplectic algorithms is proposed based on weighted residu-al method.Firstly,in the time subdomain,the corresponding integral equation of Galerkin method for Hamilton dual equation based on the idea of weighted residual method is proposed,then the generalized displacement and momentum are approximated by the same Lagrange interpolation within the time subdo-main,which are substituted into the corresponding integral equation.By numerical integration,the origi-nal initial value problem of dynamics is expressed as algebraic equations with displacement and momen-tum at the interpolation points as unknown variables.For nonlinear dynamic systems,a simple scheme of choosing initial values,which can significantly improve the computational efficiency for Newton-Raphson method,is presented.Finally,the symplecticity and performance of the proposed algorithms are dis-cussed in detail.Compared with the same order symplectic Runge-Kutta methods,the accuracy of the two methods are almost the same,but the proposed algorithms are much simpler and less computational ex-pense.The numerical results illustrate that the proposed algorithms show good performance in accuracy and efficiency.关键词
哈密顿系统/加权残值法/非线性动力学/伽辽金法/辛算法Key words
Hamilton system/weighted residual method/nonlinear dynamics/Galerkin method/sym-plectic algorithm分类
数理科学引用本文复制引用
陆克浪,富明慧,李纬华,李任飞..一种基于加权残值法的高阶辛算法[J].中山大学学报（自然科学版）,2015,(4):8-12,22,6.基金项目
国家自然科学基金资助项目（11172334）；国家自然科学基金青年科学基金资助项目（11202247）；中央高校基本科研业务费专项资金资助项目 （）
