Explicit Time-Stepping for Stiff ODEs

TL;DR

This paper introduces an explicit time-stepping strategy for stiff ODEs that adaptively uses small stabilizing steps to enable larger overall time steps, improving efficiency for many stiff problems.

Contribution

It proposes a novel adaptive explicit method that stabilizes stiff ODEs with minimal small steps, allowing larger time steps than classical methods.

Findings

Effective stabilization of stiff ODEs with small explicit steps

Significant reduction in computational cost for stiff problems

Successful application on well-known stiff test problems

Abstract

We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much larger than what is indicated by classical stability analysis. For many stiff problems the cost of the stabilizing small time steps is small, so the improvement is large. We illustrate the technique on a number of well-known stiff test problems.