A SYMPLECTIC SOLVER FOR LATTICE EQUATIONS

D.B. Duncan, C.H. Walshaw and J.A.D. Wattis

Abstract:

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.




Fri Aug 13 13:43:16 BST 2004