Volume 17, Issue 4
The Time High-Order Energy-Preserving Schemes for the Nonlocal Benjamin-Ono Equation

Chunguang Chen, Dong LiangShusen Xie

Int. J. Numer. Anal. Mod., 17 (2020), pp. 543-556.

Published online: 2020-08

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  • Abstract

The new time high-order energy-preserving schemes are proposed for the nonlocal Benjamin-Ono equation. We get the Hamiltonian system to the nonlocal model, and it is then discretized by a Fourier pseudospectral method in space and the Hamiltonian boundary value method (HBVM) in time. This approach has high order of convergence in time and conserves the total mass and energy in discrete forms. We further develop a time second-order energy-preserving scheme and a time fourth-order energy-preserving scheme for the nonlocal Benjamin-Ono equation. Numerical experiments test the proposed schemes with a single solitary wave and the interaction of two solitary waves. Results confirm the accuracy and conservation properties of the schemes.

  • Keywords

Nonlocal Benjamin-Ono equation, Hamiltonian boundary value method (HBVM), time high-order, energy preserving, Fourier pseudospectral method.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-543, author = {Chen , Chunguang and Liang , Dong and Xie , Shusen}, title = {The Time High-Order Energy-Preserving Schemes for the Nonlocal Benjamin-Ono Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {4}, pages = {543--556}, abstract = {

The new time high-order energy-preserving schemes are proposed for the nonlocal Benjamin-Ono equation. We get the Hamiltonian system to the nonlocal model, and it is then discretized by a Fourier pseudospectral method in space and the Hamiltonian boundary value method (HBVM) in time. This approach has high order of convergence in time and conserves the total mass and energy in discrete forms. We further develop a time second-order energy-preserving scheme and a time fourth-order energy-preserving scheme for the nonlocal Benjamin-Ono equation. Numerical experiments test the proposed schemes with a single solitary wave and the interaction of two solitary waves. Results confirm the accuracy and conservation properties of the schemes.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17869.html} }
TY - JOUR T1 - The Time High-Order Energy-Preserving Schemes for the Nonlocal Benjamin-Ono Equation AU - Chen , Chunguang AU - Liang , Dong AU - Xie , Shusen JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 543 EP - 556 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17869.html KW - Nonlocal Benjamin-Ono equation, Hamiltonian boundary value method (HBVM), time high-order, energy preserving, Fourier pseudospectral method. AB -

The new time high-order energy-preserving schemes are proposed for the nonlocal Benjamin-Ono equation. We get the Hamiltonian system to the nonlocal model, and it is then discretized by a Fourier pseudospectral method in space and the Hamiltonian boundary value method (HBVM) in time. This approach has high order of convergence in time and conserves the total mass and energy in discrete forms. We further develop a time second-order energy-preserving scheme and a time fourth-order energy-preserving scheme for the nonlocal Benjamin-Ono equation. Numerical experiments test the proposed schemes with a single solitary wave and the interaction of two solitary waves. Results confirm the accuracy and conservation properties of the schemes.

Chunguang Chen, Dong Liang & Shusen Xie. (2020). The Time High-Order Energy-Preserving Schemes for the Nonlocal Benjamin-Ono Equation. International Journal of Numerical Analysis and Modeling. 17 (4). 543-556. doi:
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