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Volume 25, Issue 4
Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations

Mingzhan Song, Xu Qian, Hong Zhang, Jingmin Xia & Songhe Song

DOI: 10.4208/cicp.OA-2017-0212

Commun. Comput. Phys., 25 (2019), pp. 1127-1143.

Published online: 2018-12

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  • Abstract

In this paper, we mainly propose two kinds of high-accuracy schemes for the coupled nonlinear Schrödinger (CNLS) equations, based on the Fourier pseudospectral method (FPM), the high-order compact method (HOCM) and the Hamiltonian boundary value methods (HBVMs). With periodic boundary conditions, the proposed schemes admit the global energy conservation law and converge with even-order accuracy in time. Numerical results are presented to demonstrate the accuracy, energy-preserving and long-time numerical behaviors. Compared with symplectic Runge-Kutta methods (SRKMs), the proposed schemes are assuredly more effective to preserve energy, which is consistent with our theoretical analysis.

  • Keywords

Hamiltonian boundary value methods, Fourier pseudospectral method, high-order compact method, coupled nonlinear Schrödinger equations.

  • AMS Subject Headings

37M05, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-25-1127, author = {Mingzhan Song, Xu Qian, Hong Zhang, Jingmin Xia and Songhe Song}, title = {Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {4}, pages = {1127--1143}, abstract = {

In this paper, we mainly propose two kinds of high-accuracy schemes for the coupled nonlinear Schrödinger (CNLS) equations, based on the Fourier pseudospectral method (FPM), the high-order compact method (HOCM) and the Hamiltonian boundary value methods (HBVMs). With periodic boundary conditions, the proposed schemes admit the global energy conservation law and converge with even-order accuracy in time. Numerical results are presented to demonstrate the accuracy, energy-preserving and long-time numerical behaviors. Compared with symplectic Runge-Kutta methods (SRKMs), the proposed schemes are assuredly more effective to preserve energy, which is consistent with our theoretical analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0212}, url = {http://global-sci.org/intro/article_detail/cicp/12893.html} }
TY - JOUR T1 - Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations AU - Mingzhan Song, Xu Qian, Hong Zhang, Jingmin Xia & Songhe Song JO - Communications in Computational Physics VL - 4 SP - 1127 EP - 1143 PY - 2018 DA - 2018/12 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0212 UR - https://global-sci.org/intro/article_detail/cicp/12893.html KW - Hamiltonian boundary value methods, Fourier pseudospectral method, high-order compact method, coupled nonlinear Schrödinger equations. AB -

In this paper, we mainly propose two kinds of high-accuracy schemes for the coupled nonlinear Schrödinger (CNLS) equations, based on the Fourier pseudospectral method (FPM), the high-order compact method (HOCM) and the Hamiltonian boundary value methods (HBVMs). With periodic boundary conditions, the proposed schemes admit the global energy conservation law and converge with even-order accuracy in time. Numerical results are presented to demonstrate the accuracy, energy-preserving and long-time numerical behaviors. Compared with symplectic Runge-Kutta methods (SRKMs), the proposed schemes are assuredly more effective to preserve energy, which is consistent with our theoretical analysis.

Mingzhan Song, Xu Qian, Hong Zhang, Jingmin Xia and Songhe Song. (2018). Two Kinds of New Energy-Preserving Schemes for the Coupled Nonlinear Schrödinger Equations. Communications in Computational Physics. 25 (4). 1127-1143. doi:10.4208/cicp.OA-2017-0212
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