STABILITY OF RUNGE-KUTTA METHODS FOR STIFF ORDINARY DIFFERENTIAL-EQUATIONS

This work analyzes the integration of initial value problems for stiff systems of ordinary differential equations by Runge-Kutta methods. Th e author uses the characterization of stiff initial value problems due to Kreiss: the Jacobian matrix is essentially negative dominant and s atisfies a relative Lipschitz condition. The existence and regularity of the numerical solution are established, and conditions under which the Runge-Kutta formula is stable are given.