Stability of Runge–Kutta Methods for Stiff Ordinary Differential Equations

1 August 1994

journal article
research article
Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis

Vol. 31 (4) , 1147-1168
https://doi.org/10.1137/0731060

Abstract

This work analyzes the integration of initial value problems for stiff systems of ordinary differential equations by Runge-Kutta methods. The author uses the characterization of stiff initial value problems due to Kreiss: the Jacobian matrix is essentially negative dominant and satisfies 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.

Keywords

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