Convergence of numerical schemes for the Korteweg-de Vries-Kawahara equation

Details Convergence of numerical schemes for the Korteweg-de Vries-Kawahara equation Convergence of numerical schemes for the Korteweg-de Vries-Kawahara equation

2011-06-09

arxiv.org/abs/1106.1781v1

Mathematics

Analysis of PDEs

20 Pages

Scientific paper

We are concerned with the convergence of a numerical scheme for the initial-boundary value problem associated to the Korteweg-de Vries- Kawahara equation (in short Kawahara equation), which is a transport equation perturbed by dispersive terms of 3rd and 5th order. This equation appears in several uid dynamics problems. It describes the evolution of small but ?finite amplitude long waves in various problems in uid dynamics. We prove here the convergence of both semi-discrete as well as fully-discrete ?finite di?fference schemes for the Kawahara equation. Finally, the convergence is illustratred by several examples.

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