Numerical Method for a transport equation perturbed by dispersive terms of 3rd and 5th order.

Mauricio Sepúlveda; Octavio Paulo Vera Villagrán

Vol. 13 (2006): Special Issue: Proceedings of the Conferences Valparaíso Númerico II

Articles

Numerical Method for a transport equation perturbed by dispersive terms of 3rd and 5th order.

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Mauricio Sepúlveda,
Octavio Paulo Vera Villagrán

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Mauricio Sepúlveda
Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile.

Octavio Paulo Vera Villagrán
Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile.

Published 25-02-2025

Keywords

Evolution equations,
gain in regularity,
sobolev space,
numerical methods

Abstract

We are concerned with the initial-boundary-value problem associated to the Korteweg - de Vries - Kawahara (KdVK) equation, which is a transport equation perturbed by dispersive terms of 3rd and 5th order. The (KdVK) equation appears in several fluid dynamics problems. We obtain local smoothing effects that are uniform with respect to the size of the interval. We also propose a simple finite-difference scheme for the problem and prove its stability. Finally, we give some numerical examples.

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