Work

Strong approximation of stochastic semiclassical Schrödinger equation with multiplicative noise

Year: 2024

Type: article

Abstract: We consider the stochastic nonlinear Schrödinger equation driven by a multiplicative noise in a semiclassical regime, where the Plank constant $ \varepsilon $ is small. In this regime, the solution of the equation exhibits high-frequency oscillations. We design an efficient numerical approximation by combining the spectral Galerkin method and the temporal midpoint scheme. This accurately approximates the solution, or at least of the associated physical observables. Furthermore, the strong convergence rates for the proposed numerical approximation are derived, which explicitly depend on the scaled Planck constant. This conclusion implies the semiclassical regime's admissible meshing strategies for obtaining 'correct' physical observables.

Source: Communications on Analysis and Computation

DOI: 10.3934/cac.2024022

Authors: Lihai Ji, Zhihui Liu

Institutions: Institute of Applied Physics and Computational Mathematics, Southern University of Science and Technology

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: G3525342947, G7796276536, G8002280992, G8818383366