For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge--Kutta methods and continuous-stage Runge--Kutta methods and feature a set of free parameters that offer greater flexibility and efficiency. Specifically, we demonstrate that by carefully choosing these free parameters a simplified Newton iteration applied to the integrators of order four can be parallelizable. This results in faster and more efficient integrators compared with existing fourth-order energy-preserving integrators.

翻译：针对具有非规范结构矩阵的哈密顿系统，本文提出了一种新的四阶保能量积分器系列。该积分器采用龙格-库塔方法与连续阶段龙格-库塔方法组合的形式，并包含一组可自由选择的参数，从而提供了更高的灵活性和效率。具体而言，我们证明了通过精心选择这些自由参数，应用于四阶积分器的简化牛顿迭代算法可实现并行化。与现有四阶保能量积分器相比，该方法可构建更快、更高效的积分器。