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

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.

UDC: 519.63

Received: 18.11.2013

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