Numerical integration of coupled Korteweg-de Vries System

Details Numerical integration of coupled Korteweg-de Vries System Numerical integration of coupled Korteweg-de Vries System

2002-11-28

arxiv.org/abs/math/0211453v1

Mathematics

Numerical Analysis

11 pages, 13 figures

Scientific paper

We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality by proving its stability and convergence which gives the conditions and the appropriate choice of the grid sizes. The method is applied to Hirota-Satsuma (HS) system and compared with its known explicit solution investigating the influence of initial conditions and grid sizes on accuracy. We also illustrate the method to show the effects of constants with a transition to non-integrable cases.

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