Discrete Artificial Boundary Conditions for the Korteweg-de Vries Equation

Christophe Besse (1) , Matthias Ehrhardt (2) , Ingrid Lacroix-Violet (3, 4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Bergische Universität Wuppertal
3 RAPSODI - Reliable numerical approximations of dissipative systems
4 Université de Lille, Sciences et Technologies

In this paper we consider two numerical scheme based on trapezoidal rule in time for the linearized KdV equation in one space dimension. The goal is to derive some suitable artificial boundary conditions for these two full discretization using Z-transformation. We give some numerical benchmark examples from the literature to illustrate our findings.

Mots clés: KdV equation; Numerical simulation; artificial boundary conditions

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Besse, Matthias Ehrhardt, Ingrid Lacroix-Violet. Discrete Artificial Boundary Conditions for the Korteweg-de Vries Equation. Numerical Methods for Partial Differential Equations, 2016, 35 (5), pp.1455-1484. ⟨10.1002/num.22058⟩. ⟨hal-01105043v3⟩