New Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step.

本文创新性地提出了一种基于松弛技术和扩展Runge-Kutta Nystr?m（ERKN）方法的能量守恒算法，用于求解振荡哈密顿系统。通过引入松弛参数γ，新方法（RERKN）在保持原系统能量守恒性的同时，显著提升了长期数值模拟的精度。研究不仅证明了松弛参数的存在性，还 ...

SIAM Journal on Numerical Analysis, Vol. 43, No. 3 (2006), pp. 924-948 (25 pages) Over the last few years a great effort has been made to develop monotone high order explicit Runge-Kutta methods by ...