Abstract: The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge-Kutta (RK) method is an important part of the former, and the continuous finite element method (CFEM) belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms—the regular method. Finally, numerical
experiments are given to verify the theoretical results.

Key words: equilibrium point, Hamiltonian system, energy conservation, symplecticity, finite element method, Runge-Kutta method, asymptotic stability, infection model, SARS epidemic