Stiffness Detection and Estimation of Dominant Spectra with Explicit Runge-Kutta Methods

Abstract

A new stiffness detection scheme based on explicit Runge-Kutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this technique is a worthwhile alternative to other known stiffness detection schemes, especially when the systems are large and when it is desirable to know more about the spectrum of the Jacobian than just the spectral radius.