Adaptive Stiff Solvers at Low Accuracy and Complexity

We consider here adaptive stiff solvers at low accuracy and complexity for systems of ordinary differential equations. For the adaptive algorithm we propose to use a novel monitor function given by the comparison between a measure of the local variability of the solution times the used step size and the order of magnitude of the solution. The considered stiff solvers are: a special second order Rosenbrock method with low complexity, and the classical BDF method of the same order. We use a reduced model for the production of ozone in the lower troposphere as a test problem for the proposed adaptive strategy.