Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage

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• 作者：Wensheng Tang ; ^{tangws@lsec.cc.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Guangming Lang ^{langguangming1984@126.com" class="auth_mail" title="E-mail the corresponding author} ; Xuqiong Luo ^{luoxuqiong@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hamiltonian systems ; Symplectic methods ; Continuous-stage Runge&ndash ; Kutta methods ; Continuous-stage partitioned Runge&ndash ; Kutta methods
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 August 2016
• 年：2016
• 卷：286
• 期：Complete
• 页码：279-287
• 全文大小：384 K

文摘

Hamiltonian systems, as one of the most important class of dynamical systems, are associated with a well-known geometric structure called symplecticity. Symplectic numerical algorithms, which preserve such a structure are therefore of interest. In this article, we study the construction of symplectic (partitioned) Runge–Kutta methods with continuous stage. This construction of symplectic methods mainly relies upon the expansion of orthogonal polynomials and the simplifying assumptions for (partitioned) Runge–Kutta type methods. By using suitable quadrature formulae, it also provides a new and simple way to construct symplectic (partitioned) Runge–Kutta methods in classical sense.