Structure Preserving Algorithms For The Study

In this paper we first define the jet symplectic difference schemes of the Hamiltonian systems in general symplectic structure with variable coefficients and consider the construction of jet symplectic difference schemes for classical Hamiltonian systems. In the second part we show one DEL equation which Wang has gived existent the fundamental geometric structures as well as their preservation along solutions that can be obtained directly from the variatonal principle. In particular, we prove this difference schemes are jet symplectic and use this structure to prove Noether's theorem.