On the convergence of Runge-Kutta methods for stiff nonlinear differential equations (Q1279836)

The convergence properties of general Runge-Kutta methods when are applied to a special class of stiff nonlinear initial value problems are studied. The obtained result is that under weaker assumptions on the coefficients of a Runge-Kutta method than in the theory of \(B\)-convergence, it is possible to prove convergence of the method for stiff nonlinear initial value problems. Results on the existence and uniqueness of the Runge-Kutta solution are finally described.