EFFICIENT SAV–HERMITE METHODS FOR THE NONLINEAR DIRAC EQUATION

Zhe Yu; Jie Shen

doi:10.3934/dcdsb.2022225

EFFICIENT SAV–HERMITE METHODS FOR THE NONLINEAR DIRAC EQUATION

Zhe Yu
, Jie Shen^*

^*Corresponding author for this work

Harbin Institute of Technology
Purdue University

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

1 Scopus citations

Abstract

We construct two SAV/CN–Hermite schemes for one and two dimensional nonlinear Dirac equation in this paper. Both SAV/CN methods preserve the energy and mass and an efficient and accurate scheme is proposed by Hermite approximation. The numerical analysis of error estimates is established on SAV/CN scheme. Numerical experiments confirm the expected convergence order. In addition, they are given to show the simulations of binary and ternary collisions.

Original language	English
Pages (from-to)	3428-3452
Number of pages	25
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	28
Issue number	6
DOIs	https://doi.org/10.3934/dcdsb.2022225
State	Published - Jun 2023
Externally published	Yes

Keywords

Error estimate
Nonlinear Dirac equation
SAV approximation
Spectral method

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10.3934/dcdsb.2022225

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title = "EFFICIENT SAV–HERMITE METHODS FOR THE NONLINEAR DIRAC EQUATION",

abstract = "We construct two SAV/CN–Hermite schemes for one and two dimensional nonlinear Dirac equation in this paper. Both SAV/CN methods preserve the energy and mass and an efficient and accurate scheme is proposed by Hermite approximation. The numerical analysis of error estimates is established on SAV/CN scheme. Numerical experiments confirm the expected convergence order. In addition, they are given to show the simulations of binary and ternary collisions.",

keywords = "Error estimate, Nonlinear Dirac equation, SAV approximation, Spectral method",

author = "Zhe Yu and Jie Shen",

year = "2023",

month = jun,

doi = "10.3934/dcdsb.2022225",

language = "英语",

volume = "28",

pages = "3428--3452",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

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T1 - EFFICIENT SAV–HERMITE METHODS FOR THE NONLINEAR DIRAC EQUATION

AU - Yu, Zhe

AU - Shen, Jie

PY - 2023/6

Y1 - 2023/6

N2 - We construct two SAV/CN–Hermite schemes for one and two dimensional nonlinear Dirac equation in this paper. Both SAV/CN methods preserve the energy and mass and an efficient and accurate scheme is proposed by Hermite approximation. The numerical analysis of error estimates is established on SAV/CN scheme. Numerical experiments confirm the expected convergence order. In addition, they are given to show the simulations of binary and ternary collisions.

AB - We construct two SAV/CN–Hermite schemes for one and two dimensional nonlinear Dirac equation in this paper. Both SAV/CN methods preserve the energy and mass and an efficient and accurate scheme is proposed by Hermite approximation. The numerical analysis of error estimates is established on SAV/CN scheme. Numerical experiments confirm the expected convergence order. In addition, they are given to show the simulations of binary and ternary collisions.

KW - Error estimate

KW - Nonlinear Dirac equation

KW - SAV approximation

KW - Spectral method

UR - https://www.scopus.com/pages/publications/85147915182

U2 - 10.3934/dcdsb.2022225

DO - 10.3934/dcdsb.2022225

M3 - 文章

AN - SCOPUS:85147915182

SN - 1531-3492

VL - 28

SP - 3428

EP - 3452

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 6

ER -

EFFICIENT SAV–HERMITE METHODS FOR THE NONLINEAR DIRAC EQUATION

Abstract

Keywords

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