Efficient calculations of classical trajectories and stability matrices for semiclassical theory with locally analytic integrator. The Hulme method revisited

We demonstrate that quantities such as classical paths, action integrals, s tability matrix, caustics, and so on, which are all required in semiclassic al chemical dynamics, can be integrated very efficiently by means of a loca lly analytic integrator (LAI). Hulme's collocation method is improved to ca rry out these integrations systematically. LAI solves ordinary differential equations (ODEs) by recasting the set of ODEs into a set of nonlinear equa tions. Ari individual solution in each dimension is represented in terms of an analytic function of time for a short interval. We explicitly show that the local analyticity brings about distinct advantages. (C) 2001 Elsevier Science B.V. All rights reserved.