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 Schr{\"o}dinger equations with quadratic potentials, some transport equations and some Fokker-Planck equations.

翻译：我们引入了某些通用工具来设计精确的分解方法来计算由不相容的二次二次差运算者产生的数字半组。 更确切地说,我们将这些半组作为可以有效接近的半组产品来计算,例如使用假光谱方法。 我们用具有四极潜力的磁线Schr\'o}丁格尔方程式、一些运输方程式和一些Fokker-Planck方程式的例子来突出这些新方法的效率。