We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that can be approximated efficiently, using, for example, pseudo-spectral methods. We highlight the efficiency of these new methods on the examples of the magnetic linear Schrödinger equations with quadratic potentials, some transport equations and some Fokker–Planck equations.

中文翻译：

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不均匀二次微分算子生成的半群的精确分裂方法

我们介绍了一些通用工具来设计精确的拆分方法，以计算由不均匀二次微分算子生成的数值半群。更精确地，我们将这些半群分解为可以使用例如伪谱方法有效地近似的半群的乘积。我们以具有二次势的磁性线性Schrödinger方程，一些输运方程和一些Fokker-Planck方程为例，重点介绍这些新方法的效率。