Run time estimation of the spectral radius of Jacobians

摘要

It is useful for ordinary differential equation (ODE) solvers to include an estimator of the spectral radius of the Jacobian matrix of the system of ODE's, since this determines the numerical stability of the method. Hence a knowledge of spectral radius enables the run time selection of a more efficient integrator. Some techniques for estimating spectral radius are described and compared. They include methods suitable for use with any ODE solvers, but which require additional computation. Other methods are described which are suitable with Runge-Kutta or Rosenbrock methods, and which require little extra computation.