Abstract: A jet symplectic algorithm for Euler-Lagrange systems is studied.It is shown that the discrete Euler-Lagrange (DEL) equation,which was given by the second author in 1998,has fundamental geometric structures that preserve along solutions obtained directly from the variatonal principle.It is shown that these difference schemes are jet symplectic and the Nother's theorem exists by which we give the definition of a discrete version,the momentum map.A numerical example in jet symplectic difference scheme is given.A comparison with other discretization schemes was made.

Key words: Euler-Lagrange system, jet symplectic, Noether theorem, momentum preserving