We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex coefficients and are conjugated to unitary transformations for sufficiently small values of the time step-size. New and efficient methods up to order six are constructed and tested on the linear Schr\"odinger equation.

翻译：我们分析了一类可逆分裂方法在酉群定义的线性微分方程数值时间积分中的保持性质。这些格式涉及复系数，并在时间步长足够小时共轭于酉变换。我们构造了最高达六阶的新高效方法，并在线性薛定谔方程上进行了测试。