Stability of implicit Runge-Kutta methods for nonlinear stiff differential equations (Q1114352)

The author considers implicit Runge-Kutta methods and investigates, how perturbations in the internal stages influence the numerical solution. For the derivation of the results a perturbation argument applied to a linear constant coefficient equation is used. Therefore the results are not as general as those obtained by the concept of BS-stability. On the other hand, the analysis not restricted to A-stable methods. Finally it is shown that the assumptions are general enough to include space discretized nonlinear parabolic equations (method of lines).