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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Runge-Kutta methods applied to fully implicit differential-algebraic equations of index $1$
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by Anne Kværnø PDF
Math. Comp. 54 (1990), 583-625 Request permission

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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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 54 (1990), 583-625
  • MSC: Primary 65L06
  • DOI: https://doi.org/10.1090/S0025-5718-1990-1010600-8
  • MathSciNet review: 1010600