Gauss–Seidel Iteration for Stiff ODES from Chemical Kinetics

A simple Gauss–Seidel technique is proposed that exploits the special form of the chemical kinetics equations. Classical Aitken extrapolation is applied to accelerate convergence. The technique is meant for implementation in stiff solvers that are used in long range transport air pollution codes using operator splitting. Splitting necessarily gives rise to a great deal of integration restarts. Because the Gauss–Seidel iteration works matrix free, it has much less overhead than the modified Newton method. Start-up costs therefore can be kept low with this technique. Preliminary promising numerical results are presented for a prototype of a second order backward differentiation formula (BDF) solver applied to a stiff ordinary differential equation (ODE) from atmospheric chemistry. A favourable comparison with the general purpose BDF code DASSL is included. The matrix free technique may also be of interest for other chemically reacting fluid flow problems.