Abstract
In this paper we study the efficient solution of the well-known Korteweg–de Vries equation, equipped with periodic boundary conditions. A Fourier–Galerkin space semi-discretization at first provides a large-size Hamiltonian ODE problem, whose solution in time is then carried out by means of energy-conserving methods in the HBVM class (Hamiltonian Boundary Value Methods). The efficient implementation of the methods for the resulting problem is also considered and several numerical examples are reported.
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