Growth models often give rise to saddle-point stable dynamic systems with multi-dimensional stable manifolds. It is argued that standard solution procedures used to numerically approximate the transition process are generally inadequate when the (stable) eigenvalues differ substantially in...

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 multi-dimensional systems with stable eigenvalues...

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 multi-dimensional systems with stable eigenvalues...

We present a non-linear solution method of saddlepoint dynamics in discrete time optimization problems. It is based on the backward attractivity of the stable manifold and is very easy to implement. After an introduction to the general method we present two applications. First we consider the...

Economists frequently confine themselves to the qualitative analysis of continuous optimization problems or they restrict their quantitative analysis to inaccurate methods like linearization around the steady state. The fact that the solution is characterized by an inherently unstable adjustment...

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 multi-dimensional systems with stable eigenvalues...