Explicit Time-Stepping for Stiff ODEs
This work addresses the computational bottleneck of solving stiff ODEs, offering a practical improvement for scientists and engineers who rely on ODE solvers.
The authors propose an explicit time-stepping strategy for stiff ODEs that uses adaptive small stabilizing steps to allow much larger time steps than classical stability limits, achieving significant speedups on several test problems.
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.