Work

Time Splitting and Error Estimates for Nonlinear Schrödinger Equations with a Potential

Year: 2025

Type: article

Abstract: We consider the nonlinear Schrödinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity error estimates for the time discretization corresponding to an adapted Lie-Trotter splitting scheme. The proof is based on tools from spectral theory and pseudodifferential calculus in order to obtain various estimates on the spectral localization, including discrete Strichartz estimates which support the nonlinear analysis.

Source: Foundations of Computational Mathematics

DOI: 10.1007/s10208-025-09727-5

Author: Rémi Carles

Institutions: Centre National de la Recherche Scientifique, Institut de recherche mathématique de Rennes

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,290

Funder: Agence Nationale de la Recherche