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We prove convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\in H^3({\mathbb {R}})$, the scheme is shown to converge to a classical solution, and if the regularity of the initial data is less, $u_0\in L^2({\mathbb {R}}...

Convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation