# Numerical Nightmares in a Metastable System

**J. Carr, D.B. Duncan, and C.H. Walshaw**

### Abstract:

Using the Becker-Döring cluster equations as an example, we highlight
some of the problems that can arise in the numerical approximation
of dynamical systems with slowly varying solutions. We describe the
Becker-Döring model, summarise some of its properties and construct
a numerical approximation which allows accurate and efficient computation
of solutions in the long, slowly varying metastable phase. We use the
approximation to obtain test results and discuss the clear relationship
between them and the equilibrium solutions of the Becker-Döring equations.

**Key words.**
Metastability, Becker-Döring cluster equations, numerical approximation,
rounding error, differential algebraic equation.

* *

Fri Aug 13 13:43:11 BST 2004