Abstract: By using the central difference quotient operator for (∂²)/(∂x²) and the diagonal Padé approximation of exp t, two kinds of symplectic schemes which have accuracy O(Δx²+ Δt^2l) and O(Δx⁴+ Δt^2l), respectively, can be attained for wave partial differential equation. Two iterative methods are described for the linear systems formed from the above schemes. Their conditions of convergence are given for l=1,2,3,4. The numerical experiments demonstrate that the symplectic algorithm have efficiency and both methods are convergent.

Key words: Hamiltonian systems, symplectic difference schemes, iterative methods, conditions of convergence