Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous systems and, in addition, are readily implementable on modern digital computers.
Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous systems and, in addition, are readily implementable on modern digital computers.
For Calogero and Toda dynamical equations two numerical methods of arbitrary high order, conserving the Hamiltonian are developed. The methods consist of modifications of conventional polynomial extrapolation with the Gragg method used as a basic method. The theoretical study is confirmed by a number of numeiical examples.
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