We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.

中文翻译：

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非线性演化方程自适应积分的实用分裂方法。第一部分：优化方案和方案对的构建

我们对为演化方程的数值积分构建有效的高阶分裂方法这一主题提出了许多新的贡献。特定的方案是通过设置和求解分裂系数的多项式系统来构建的。为此，我们使用并修改了一种最近的方法来为一大类分裂生成这些系统。特别地，构建了旨在用于自适应积分器的各种类型的方案对。