Convergence of Runge-Kutta methods for differential-algebraic systems of index 3 Original Research Article

This article deals with convergence results of stiffly accurate implicit Runge-Kutta methods when applied to differential-algebraic equations of index 3 in Hessenberg form. Under certain hypotheses global superconvergence is shown, proving a result conjectured by Hairer, Lubich and Roche. Numerical examples are provided which illustrate the theoretical results.