Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators

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.