Arbitrary order, Hamiltonian conserving numerical solutions of Calogero and Toda systems (Q811095)

Two numerical methods - of arbitrary high order - that yield numerical solutions conserving the Hamiltonian for a Calogero system and a Toda lattice are developed. The methods are based on modifications of conventional polynomial extrapolation for which the Gragg method is used as a basic method. Some examples are considered, from them resulting that the proposed high order methods yield numerical solutions conserving the Hamiltonian exactly and giving at least as good approximations to the exact solutions as those obtained by conventional polynomial extrapolation.