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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 1, Pages 36–45 (Mi sjim817)  
Numerical modeling of the integro-differential Korteweg–de Vries–Burgers equation

N. I. Gorbenko

Institute of Computational Mathematics and Mathematical Geophysics, 15 Lavrent'ev av., 630090 Novosibirsk
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Abstract: We develop explicit and implicit schemes that are based on the finite volume method for the Korteweg–de Vries–Burgers equation which become multisymplectic for the Korteweg–de Vries equation. The resulting schemes have better stability on long-term calculations. An algorithm for calculating the Duhamel integral with a fixed amount of memory is proposed. The results of numerical experiments are presented.
Keywords: integral-differential equation, Hamiltonian, multisymplectic, explicit and implicit schemes, numerical experiment.
Received: 18.11.2013
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: N. I. Gorbenko, “Numerical modeling of the integro-differential Korteweg–de Vries–Burgers equation”, Sib. Zh. Ind. Mat., 17:1 (2014), 36–45
Citation in format AMSBIB
\Bibitem{Gor14}
\by N.~I.~Gorbenko
\paper Numerical modeling of the integro-differential Korteweg--de Vries--Burgers equation
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 1
\pages 36--45
\mathnet{http://mi.mathnet.ru/sjim817}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3379252}
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