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

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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@Article{CiCP-25-1127, author = {}, 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 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 & Songhe Song. (2020). 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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