The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients. We show that schemes of this type exhibit a good long time behavior when applied to linear unitary and linear Hamiltonian systems, in contrast with other methods based on complex coefficients, and study in detail their preservation properties. We also present new schemes within this class up to order 6 that exhibit a better efficiency than state-of-the-art splitting methods with real coefficients for some classes of problems.

翻译：本文提出并分析了一类新的交替共轭分裂方法。该类方法通过将含复系数的给定组合格式与具有复共轭系数的相同组合格式进行级联而构建。研究表明，与其它基于复系数的方法相比，此类格式在应用于线性酉系统和线性哈密顿系统时展现出良好的长时间特性，并详细分析了其保结构性质。此外，我们提出了该类别中直至六阶的新格式，针对某些问题类别，这些格式较当前最先进的实系数分裂方法具有更优的计算效率。