Runge-Kutta methods revisited for a class of structured strangeness-free differential-algebraic equations

Abstract

Numerical methods for a class of nonlinear differential-algebraic equations (DAEs) of the strangeness-free form are investigated. Half-explicit and implicit Runge-Kutta methods are revisited as they are applied to a reformulated form of the original DAEs. It is shown that the methods preserve the same convergence order and the same stability properties as if they were applied to ordinary differential equations (ODEs). Thus, a wide range of explicit Runge-Kutta methods and implicit ones, which are not necessarily stiffly accurate, can efficiently solve the class of DAEs under consideration. Implementation issues and a perturbation analysis are also discussed. Numerical experiments are presented to illustrate the theoretical results.