Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 99, Issue 5, Pages 877-894Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2021.1940978
Keywords
Fractional nonlinear Schrodinger equation; structure-preserving algorithms; invariant energy quadratization; Runge-Kutta method; explicit conservative schemes
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Funding
- National Key Research and Development Project of China [2017YFC0601505, 2018YFC1504205]
- National Natural Science Foundation of China [11771213, 11971416, 11971242]
- Major Projects of Natural Sciences of University in Jiangsu Province of China [18KJA110003]
- Program for Scientific and Technological Innovation Talents in Universities of Henan Province [19HASTIT025]
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This paper aims to construct a class of high-order explicit conservative schemes for the space fractional nonlinear Schrodinger equation by combining the invariant energy quadratization method and Runge-Kutta method. Numerical experiments demonstrate the conservative properties, convergence orders, and long time stability of the proposed schemes, which provide a promising approach for solving the equation.
The paper aims to construct a class of high-order explicit conservative schemes for the space fractional nonlinear Schrodinger 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.
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