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数值时间积分线性微分方程（定义于酉群中）时保持的性质。这些格式包含复系数，并且对于足够小的时间步长，它们共轭于酉变换。我们构建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。