A Galerkin FEM for Riesz space-fractional CNLS

Xiaogang Zhu; Yufeng Nie; Zhanbin Yuan; Jungang Wang; Zongze Yang

doi:10.1186/s13662-019-2278-y

A Galerkin FEM for Riesz space-fractional CNLS

Xiaogang Zhu, Yufeng Nie, Zhanbin Yuan, Jungang Wang, Zongze Yang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In quantum physics, fractional Schrödinger equation is of particular interest in the research of particles on stochastic fields modeled by the Lévy processes, which was derived by extending the Feynman path integral over the Brownian paths to a path integral over the trajectories of Lévy fights. In this work, a fully discrete finite element method (FEM) is developed for the Riesz space-fractional coupled nonlinear Schrödinger equations (CNLS), conjectured with a linearized Crank–Nicolson discretization. The error estimate and mass conservative property are discussed. It is showed that the proposed method is decoupled and convergent with optimal orders in L²-sense. Numerical examples are performed to support our theoretical results.

Original language	English
Article number	329
Journal	Advances in Difference Equations
Volume	2019
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2278-y
State	Published - 1 Dec 2019

Keywords

Convergent analysis
FEM
Space-fractional CNLS

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title = "A Galerkin FEM for Riesz space-fractional CNLS",

abstract = "In quantum physics, fractional Schr{\"o}dinger equation is of particular interest in the research of particles on stochastic fields modeled by the L{\'e}vy processes, which was derived by extending the Feynman path integral over the Brownian paths to a path integral over the trajectories of L{\'e}vy fights. In this work, a fully discrete finite element method (FEM) is developed for the Riesz space-fractional coupled nonlinear Schr{\"o}dinger equations (CNLS), conjectured with a linearized Crank–Nicolson discretization. The error estimate and mass conservative property are discussed. It is showed that the proposed method is decoupled and convergent with optimal orders in L2-sense. Numerical examples are performed to support our theoretical results.",

keywords = "Convergent analysis, FEM, Space-fractional CNLS",

author = "Xiaogang Zhu and Yufeng Nie and Zhanbin Yuan and Jungang Wang and Zongze Yang",

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T1 - A Galerkin FEM for Riesz space-fractional CNLS

AU - Zhu, Xiaogang

AU - Nie, Yufeng

AU - Yuan, Zhanbin

AU - Wang, Jungang

AU - Yang, Zongze

PY - 2019/12/1

Y1 - 2019/12/1

N2 - In quantum physics, fractional Schrödinger equation is of particular interest in the research of particles on stochastic fields modeled by the Lévy processes, which was derived by extending the Feynman path integral over the Brownian paths to a path integral over the trajectories of Lévy fights. In this work, a fully discrete finite element method (FEM) is developed for the Riesz space-fractional coupled nonlinear Schrödinger equations (CNLS), conjectured with a linearized Crank–Nicolson discretization. The error estimate and mass conservative property are discussed. It is showed that the proposed method is decoupled and convergent with optimal orders in L2-sense. Numerical examples are performed to support our theoretical results.

AB - In quantum physics, fractional Schrödinger equation is of particular interest in the research of particles on stochastic fields modeled by the Lévy processes, which was derived by extending the Feynman path integral over the Brownian paths to a path integral over the trajectories of Lévy fights. In this work, a fully discrete finite element method (FEM) is developed for the Riesz space-fractional coupled nonlinear Schrödinger equations (CNLS), conjectured with a linearized Crank–Nicolson discretization. The error estimate and mass conservative property are discussed. It is showed that the proposed method is decoupled and convergent with optimal orders in L2-sense. Numerical examples are performed to support our theoretical results.

KW - Convergent analysis

KW - FEM

KW - Space-fractional CNLS

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DO - 10.1186/s13662-019-2278-y

M3 - 文章

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SN - 1687-1839

VL - 2019

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 329

ER -

A Galerkin FEM for Riesz space-fractional CNLS

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Keywords

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