Volume 48, pp. 131-155, 2018.

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

Vu Hoang Linh and Nguyen Duy Truong

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.

Full Text (PDF) [385 KB]

Key words

differential-algebraic equation, strangeness-free form, Runge-Kutta method, half-explicit method, convergence, stability

AMS subject classifications

65L80, 65L05, 65L06, 65L20

Links to the cited ETNA articles

[14]Vol. 26 (2007), pp. 385-420 Peter Kunkel and Volker Mehrmann: Stability properties of differential-algebraic equations and spin-stabilized discretizations

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