An easily implementable fourth-order method for the time integration of wave problems

Abstract We are concerned with the time-integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions. A method is suggested that, while being as easily implementable as the standard implicit mid-point rule, is fourth-order accurate. The new method is symplectic so that it is very well suited for long-time integrations of problems with a Hamiltonian structure. Numerical experiments are reported that refer to a fourth-order Galerkin space discretization of the Korteweg-de Vries equation and to a pseudospectral space discretization of the same equation.

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