Eventual periodicity of the forced oscillations for a Korteweg–de Vries type equation on a bounded domain using a sinc collocation method

Abstract

We demonstrate numerically the eventual time periodicity of solutions u ( . , t ) to the Korteweg–de Vries type equation with periodic forcing at one end using the sinc-collocation method. This method approximates the space dimension of the solution with a cardinal expansion of sinc functions, thus allowing the avoidance of a costly finite difference grid for a third order boundary value problem. The first order time derivative is approximated with a θ -weighted finite difference method. The sinc-collocation method was found to be more robust and more efficient than other numerical schemes when applied to this problem.