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