Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

2008/12/18 by Walter H. Aschbacher, Aschbacher, Walter H.
Mathematics · Physics and Astronomy · #35J60 #35Q35 #35Q40 #65M60 #65N30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0812.3606

openalex publication_date 2008/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

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