Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators

Joackim Bernier (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Splitting methods; Quadratic differential operators

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Joackim Bernier. Exact splitting methods for semigroups generated by inhomogeneous quadratic differential operators. Foundations of Computational Mathematics, 2021. ⟨hal-02425591v2⟩