A NOTE ON THE CONVERGENCE OF A CRANK-NICOLSON SCHEME FOR THE KDV EQUATION

摘要

The aim of this paper is to establish the convergence of a fully discrete Crank-Nicolson type Galerkin scheme for the Cauchy problem associated to the KdV equation. The convergence is achieved for initial data in L-2, and we show that the scheme converges strongly in L-2(0, T; L-log(2) (R)) to a weak solution for some T > 0. Finally, the convergence is illustrated by a numerical example.