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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Vydáno v:International journal of computer mathematics Ročník 99; číslo 5; s. 877 - 894
Hlavní autoři: Fu, Yayun, Shi, Yanhua, Zhao, Yanmin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 04.05.2022
Taylor & Francis Ltd
Témata:
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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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2021.1940978