CAJ | 학술논문

利用常微分方程的连续有限元法,结合函数的M-型展开,对非线性哈密尔顿系统证明了连续一、二次有限元分在3阶量、5阶量意义下近似保辛,且保持能量守恒.在数值实验中结合庞加莱截面,哈密尔顿混沌数值试验结果与理论相吻合.
이용상미분방정적련속유한원법,결합함수적M-형전개,대비선성합밀이돈계통증명료련속일、이차유한원분재3계량、5계량의의하근사보신,차보지능량수항.재수치실험중결합방가래절면,합밀이돈혼돈수치시험결과여이론상문합.
By applying the continuous finite element methods for ordinary differential equations and combine M-type function unfold, the linear element are proved an approximately symplectic method which is accurate of third order to their symplectic structure and the quadratic element are proved an approximately symplectic method which is accurate of fifth order to their symplectic structure, as well as energy conservative. Combine Poincar(e) section, the numerical results of Hamiltonian chaos agree with the theory.