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：针对具有非标准结构矩阵的哈密顿系统，本文提出了一类新的四阶保能量积分器。该类积分器采用龙格-库塔方法与连续阶段龙格-库塔方法组合的形式，并包含一组自由参数，从而具有更高的灵活性与计算效率。具体而言，我们证明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可实现并行化。与现有四阶保能量积分器相比，由此产生的积分器更加快速高效。