A split-step finite element method for the space-fractional Schrödinger equation in two dimensions

Autor:	Xiaogang Zhu, Haiyang Wan, Yaping Zhang
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	Space-fractional Schrödinger equation Split-step scheme Finite element scheme Error estimate Medicine Science
Zdroj:	Scientific Reports, Vol 14, Iss 1, Pp 1-20 (2024)
Druh dokumentu:	article
ISSN:	2045-2322
DOI:	10.1038/s41598-024-75547-2
Popis:	Abstract In this article, we propose a split-step finite element method (FEM) for the two-dimensional nonlinear Schrödinger equation (NLS) with Riesz fractional derivatives in space. The space-fractional NLS is first spatially discretized by finite element scheme and the semi-discrete variational scheme is obtained. We prove that it maintains the mass and energy conservation laws. Then, we establish a fully discrete split-step finite element scheme for the considered problem, which avoids the iteration at each time layer, thereby significantly reducing computational cost. The discrete mass conservation property and error estimate of this split-step finite element scheme is derived. Finally, illustrative tests and the numerical simulation of dynamic of wave solutions are included to confirm its effectiveness and capability.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/c5034375e86443bcbb09eb0be5aeb183 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
Nepřihlášeným uživatelům se plný text nezobrazuje	K zobrazení výsledku je třeba se přihlásit.