Abstract
We propose a symplectic finite difference scheme for the Boussinesq equations with sixth order dispersion terms. This scheme conserves exactly the discrete mass and approximately with error \(O(h^2+\tau ^2)\) the discrete Hamiltonian. The numerical experiments for quadratic and cubic nonlinearity confirm the theoretical results.
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Acknowledgements
This work is partially supported by the project DFNP 17-30 of the Program for young scientists’ career development of Bulgarian Academy of Sciences and the Bulgarian Science Fund under grant DNTS/Russia 02/7.
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Vucheva, V., Kolkovska, N. (2021). A Symplectic Numerical Method for the Sixth Order Boussinesq Equation. In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2018. Studies in Computational Intelligence, vol 961. Springer, Cham. https://doi.org/10.1007/978-3-030-71616-5_37
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DOI: https://doi.org/10.1007/978-3-030-71616-5_37
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