Simos T E, Vigo-Aguiar Jesus
Department of Computer Science and Technology, Faculty of Science and Technology, University of Peloponnese, University Campus, GR-221 00 Tripolis, Greece.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jan;67(1 Pt 2):016701. doi: 10.1103/PhysRevE.67.016701. Epub 2003 Jan 8.
In this paper a procedure for constructing efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the exponential fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge-Kutta-Nyström second-order algebraic exponentially fitted method is developed. We give explicitly the symplecticness conditions for the modified Runge-Kutta-Nyström method. We also give the exponential fitting and trigonometric fitting conditions. Numerical results indicate that the present method is much more efficient than the "classical" symplectic Runge-Kutta-Nyström second-order algebraic method introduced by M.P. Calvo and J.M. Sanz-Serna [J. Sci. Comput. (USA) 14, 1237 (1993)]. We note that the present procedure is appropriate for all near-unimodal systems.
本文介绍了一种为哈密顿问题构造高效辛积分器的方法。该方法基于指数拟合技术和辛性条件的结合。基于此方法，开发了一种简单的修正龙格 - 库塔 - 奈斯特勒姆二阶代数指数拟合方法。我们明确给出了修正龙格 - 库塔 - 奈斯特勒姆方法的辛性条件。我们还给出了指数拟合和三角拟合条件。数值结果表明，本方法比M.P. 卡尔沃和J.M. 桑斯 - 塞尔纳 [《科学计算杂志》（美国）14, 1237 (1993)] 引入的“经典”辛龙格 - 库塔 - 奈斯特勒姆二阶代数方法效率高得多。我们注意到本方法适用于所有近单峰系统。
