Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure

Abstract

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise to a continuum of stationary equilibria. (2) The application of the procedure is fairly user friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the infinite time horizon, which usually underlies optimal control problems in economics. As an illustrative application, we simulate the transition process of the Jones (1995) and the Lucas (1988) model.

Keywords: transitional dynamics, continuous time growth models, saddle-point problems, multi-dimensional stable manifolds

JEL Classification: C61, C63, O40