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Runge-Kutta methods applied to fully implicit differential-algebraic equations of index $ 1$


Author: Anne Kværnø
Journal: Math. Comp. 54 (1990), 583-625
MSC: Primary 65L06
DOI: https://doi.org/10.1090/S0025-5718-1990-1010600-8
MathSciNet review: 1010600
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Abstract: In this paper we study the order of Runge-Kutta methods applied to differential-algebraic equations of index one. We derive general order conditions for the local order $ {k_L}$, and give a convergence result, which shows that the order $ {k_G}$ of the global error satisfies $ {k_G} \geq {k_L} - 1$. We also describe some numerical experiments, which are in agreement with our results.


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DOI: https://doi.org/10.1090/S0025-5718-1990-1010600-8
Article copyright: © Copyright 1990 American Mathematical Society