D.B. Duncan, C.H. Walshaw and J.A.D. Wattis
We describe an Ordinary Differential Equation solver for lattice dynamics equations in Hamiltonian form, which is more accurate, more efficient and easier to programme than the commonly used Runge-Kutta methods. An important feature of the solver is that it preserves the symplectic nature of the differential equations. We illustrate the application of scheme in a variety of examples of one and two space dimensional lattices, including the Toda lattice and a discrete version of the K.P. equation. We also show some comparisons with standard Runge-Kutta methods.