Stability of Runge-Kutta methods for
stiff ordinary differential equations
Abstract: This work analyzes the integration of initial value
problems for stiff systems of ordinary differential equations by Runge-Kutta
methods. We use the characterization of stiff initial value problems due to
Kreiss: the Jacobian matrix is essentially negative dominant and satisfies a
relative Lipschitz condition. We establish the existence and regularity of
the numerical solution, and give conditions under which the Runge-Kutta
formula is stable.
Available by anonymous ftp from ftp.math.iastate.edu in the directory
pub/alex/preprints/rks