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Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type

机译：高斯型六阶对称辛辛指数拟合的改进的Runge-Kutta方法

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摘要

The construction of symmetric and symplectic exponentially fitted modified Runge-Kutta (RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. In a previous paper [H. Van de Vyver, A fourth order symplectic exponentially fitted integrator, Comput. Phys. Comm. 176 (2006) 255-262] a two-stage fourth-order symplectic exponentially fitted modified RK method has been proposed. Here, two three-stage symmetric and symplectic exponentially fitted integrators of Gauss type, either with fixed nodes or variable nodes, are derived. The algebraic order of the new integrators is also analyzed, obtaining that they possess sixth-order as the classical three-stage RK Gauss method. Numerical experiments with some oscillatory problems are presented to show that the new methods are more efficient than other symplectic RK Gauss codes proposed proposed in the scientific literature. (c) 2008 Elsevier B.V. All rights reserved.
机译：考虑构造对称和辛指数拟合的改进的Runge-Kutta（RK）方法，以求解含振动解的哈密顿系统的数值积分。在以前的论文中[H. Van de Vyver，四阶辛指数拟合的积分器，Comput。物理通讯[176（2006）255-262]提出了一种两阶段的四阶辛指数拟合的改进RK方法。在此，推导了两个具有固定节点或可变节点的高斯型三级对称且辛指数拟合的积分器。还对新积分器的代数阶进行了分析，得出它们具有六阶作为经典的三阶RK高斯方法。提出了具有振荡问题的数值实验，表明该新方法比科学文献中提出的其他辛辛RK Gauss码更有效。 （c）2008 Elsevier B.V.保留所有权利。

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