Extrapolation of symplectic methods for Hamiltonian problems
Recently, symplectic Runge-Kutta methods used with constant stepsize have been shown to exhibit linear error growth when applied to certain classes of Hamiltonian systems over long time intervals. This paper addresses the problem of the length of the integration interval over which extrapolation will improve the numerical solution. The authors consider two models of the extrapolation of symplectic and symmetric numerical integrators. In the passive mode, two solution sequences are computed with different stepsizes independently and extrapolation is performed whenever output is required. In the active mode, the extrapolation is carried out at each step and the extrapolated solution is then propagated. Both modes of extrapolation are studied in detail and compared for the simple harmonic oscillator.
scientific article; zbMATH DE number 1462298