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We demonstrate numerically the eventual time-periodicity of the solutions of the Korteweg-de Vries equation with periodic forcing at the boundary 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 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.
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Stander Symposium poster
Haynes, Nicholas D., "Numerical solution of the KdV equation with periodic boundary conditions using the sinc-collocation method" (2013). Stander Symposium Posters. 267.