Martin Arnold
Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index 2
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

65L05 Initial value problems

Abstract: Usually the straightforward generalization of explicit
Runge--Kutta methods for ordinary differential equations to
half-explicit methods for differential-algebraic systems of
index 2 results in methods of order {$q\leq 2$}.
The construction of higher order methods is simplified
substantially by a slight modification of the method
combined with an improved strategy for the computation of
the algebraic solution components. We give order conditions
up to order {$q=5$} and study the convergence of these methods.
Based on the fifth order method of Dormand and Prince a
half-explicit Runge--Kutta method of order {$q=5$} is
constructed that requires the solution of 6 systems of
nonlinear equations per step of integration.
Keywords: differential-algebraic systems, half-explicit methods, explicit Runge-Kutta methods