Explicit high-order structure-preserving algorithms for the two-dimensional fractional nonlinear Schrödinger equation

The paper aims to construct a class of high-order explicit conservative schemes for the space fractional nonlinear Schrödinger equation by combing the invariant energy quadratization method and Runge-Kutta method. We first derive the Hamiltonian formulation of the equation, and obtain a new equivale...

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Vydané v:	International journal of computer mathematics Ročník 99; číslo 5; s. 877 - 894
Hlavní autori:	Fu, Yayun, Shi, Yanhua, Zhao, Yanmin
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Abingdon Taylor & Francis 04.05.2022 Taylor & Francis Ltd
Predmet:	Algorithms Approximation Discrete systems Equivalence explicit conservative schemes Fractional nonlinear Schrödinger equation invariant energy quadratization Runge-Kutta method Schrodinger equation Spectral methods structure-preserving algorithms
ISSN:	0020-7160, 1029-0265
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Abstract	The paper aims to construct a class of high-order explicit conservative schemes for the space fractional nonlinear Schrödinger equation by combing the invariant energy quadratization method and Runge-Kutta method. We first derive the Hamiltonian formulation of the equation, and obtain a new equivalent system via introducing a scalar variable. Then, we propose a semi-discrete conservative system by using the Fourier pseudo-spectral method to approximate the equivalent system in space. Further applying the fourth-order modified Runge-Kutta method to the semi-discrete system gives two classes of schemes for the equation. One scheme preserves the energy while the other scheme conserves the mass. Numerical experiments are provided to demonstrate the conservative properties, convergence orders and long time stability of the proposed schemes.
AbstractList	The paper aims to construct a class of high-order explicit conservative schemes for the space fractional nonlinear Schrödinger equation by combing the invariant energy quadratization method and Runge-Kutta method. We first derive the Hamiltonian formulation of the equation, and obtain a new equivalent system via introducing a scalar variable. Then, we propose a semi-discrete conservative system by using the Fourier pseudo-spectral method to approximate the equivalent system in space. Further applying the fourth-order modified Runge-Kutta method to the semi-discrete system gives two classes of schemes for the equation. One scheme preserves the energy while the other scheme conserves the mass. Numerical experiments are provided to demonstrate the conservative properties, convergence orders and long time stability of the proposed schemes.
Author	Shi, Yanhua Zhao, Yanmin Fu, Yayun
Author_xml	– sequence: 1 givenname: Yayun surname: Fu fullname: Fu, Yayun organization: School of Science, Xuchang University – sequence: 2 givenname: Yanhua surname: Shi fullname: Shi, Yanhua organization: School of Science, Xuchang University – sequence: 3 givenname: Yanmin surname: Zhao fullname: Zhao, Yanmin email: zhaoym@lsec.cc.ac.cn organization: School of Science, Xuchang University
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SubjectTerms	Algorithms Approximation Discrete systems Equivalence explicit conservative schemes Fractional nonlinear Schrödinger equation invariant energy quadratization Runge-Kutta method Schrodinger equation Spectral methods structure-preserving algorithms
Title	Explicit high-order structure-preserving algorithms for the two-dimensional fractional nonlinear Schrödinger equation
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