2019/12/31 by Joackim Berniér, Bernier, Joackim
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1912.13219
openalex publication_date 2019/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.