Formal energy of symplectic scheme for Hamiltonian systems and its applications (II)

In this paper, for 4-fold and 8-fold compositions of symplectic schemes, the authors obtain the formulae for calculation of the first three terms of the power series in stepsize of their formal energies. Utilizing the special properties of revertible schemes, the authors construct higher order revertible symplectic schemes for general Hamiltonian systems only through formal energies. From any order s (even) to order s + 2, a determining conclusion is obtained. And from any order s (even) to order s + 4, an algebraic equation system, when s is evaluated whose solution gives a rise by 4 in order, is about to be set up. As examples, for the cases of s = 2 and s = 4, the numerical results are to be gained.