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 orderq≤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 orderq=5 and study the convergence of these methods. Based on the fifth order method of Dormand and Prince the fifth order half-explicit Runge-Kutta method HEDOP5 is constructed that requires the solution of 6 systems of nonlinear equations per step of integration.
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Communicated by Syvert Nørsett.
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Arnold, M. Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index 2. Bit Numer Math 38, 415–438 (1998). https://doi.org/10.1007/BF02510252
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DOI: https://doi.org/10.1007/BF02510252