Volume 9, Issue 5
Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation

Qi Hong, Yushun Wang & Qikui Du

Adv. Appl. Math. Mech., 9 (2017), pp. 1206-1224.

Published online: 2018-05

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  • Abstract

In this paper, based on the multi-symplectic formulations of the generalized fifth-order KdV equation and the averaged vector field method, two new energy-preserving methods are proposed, including a new local energy-preserving algorithm which is independent of the boundary conditions and a new global energy-preserving method. We prove that the proposed methods preserve the energy conservation laws exactly. Numerical experiments are carried out, which demonstrate that the numerical methods proposed in the paper preserve energy well.

  • Keywords

Generalized fifth-order KdV equation, local energy-preserving, global energy-preserving, average vector field, Fourier pseudospectral.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1206, author = {Qi Hong , and Yushun Wang , and Du , Qikui}, title = {Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {5}, pages = {1206--1224}, abstract = {

In this paper, based on the multi-symplectic formulations of the generalized fifth-order KdV equation and the averaged vector field method, two new energy-preserving methods are proposed, including a new local energy-preserving algorithm which is independent of the boundary conditions and a new global energy-preserving method. We prove that the proposed methods preserve the energy conservation laws exactly. Numerical experiments are carried out, which demonstrate that the numerical methods proposed in the paper preserve energy well.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0044}, url = {http://global-sci.org/intro/article_detail/aamm/12197.html} }
TY - JOUR T1 - Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation AU - Qi Hong , AU - Yushun Wang , AU - Du , Qikui JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1206 EP - 1224 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0044 UR - https://global-sci.org/intro/article_detail/aamm/12197.html KW - Generalized fifth-order KdV equation, local energy-preserving, global energy-preserving, average vector field, Fourier pseudospectral. AB -

In this paper, based on the multi-symplectic formulations of the generalized fifth-order KdV equation and the averaged vector field method, two new energy-preserving methods are proposed, including a new local energy-preserving algorithm which is independent of the boundary conditions and a new global energy-preserving method. We prove that the proposed methods preserve the energy conservation laws exactly. Numerical experiments are carried out, which demonstrate that the numerical methods proposed in the paper preserve energy well.

Qi Hong, Yushun Wang & Qikui Du. (2020). Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation. Advances in Applied Mathematics and Mechanics. 9 (5). 1206-1224. doi:10.4208/aamm.OA-2016-0044
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