On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations

Xavier Antoine (1, 2) , Qinglin Tang (3, 4) , Jiwei Zhang (5)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 CUHK - The Chinese University of Hong Kong [Hong Kong]
4 SCU - Sichuan University [Chengdu]
5 CSRC - Beijing Computational Science Research Center [Beijing]

The purpose of this paper is to discuss some recent developments concerning the numerical simulation of space and time fractional Schrödinger and Gross-Pitaevskii equations. In particular, we address some questions related to the discretization of the models (order of accuracy and fast implementation) and clarify some of their dynamical properties. Some numerical simulations illustrate these points.

Mots clés: conservation properties; fractional Schrödinger equation; discretization schemes; dynamical laws; accuracy order; fast implementation; fractional Gross-Pitaevskii equations

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

Xavier Antoine, Qinglin Tang, Jiwei Zhang. On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations. International Journal of Computer Mathematics, 2018, 95 (6-7), pp.1423-1443. ⟨10.1080/00207160.2018.1437911⟩. ⟨hal-01649721⟩