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W. Auzinger, A. Eder, R. Frank:
"Convergence theory for implicit Runge-Kutta methods applied to a one-parameter family of stiff autonomous differential equations";
Report for Technical Report No.123/98, Institut für Angewandte und Numerische Mathematik; 1998.

The intention of this paper is to extend the convergence concepts for discretization methods applied to nonlinear stiff problems. First a one-paremeter family of stiff autonomous differential equations is introduced, where stiffness is axiomatically characterized in geometric terms. Then the discretization methods are analyzed, where we restrict our considerations to the implicit Runge-Kutta methods of the type Radau Ia, IIa and Gauss. For these methods we prove the solvability of the algebraic equations and derive global error bounds.