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Specialized Runge-Kutta methods for index $ 2$ differential-algebraic equations


Author: Laurent O. Jay
Journal: Math. Comp. 75 (2006), 641-654
MSC (2000): Primary 65L05, 65L06, 65L80
DOI: https://doi.org/10.1090/S0025-5718-05-01809-0
Published electronically: December 19, 2005
MathSciNet review: 2196984
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Abstract: We consider the numerical solution of systems of semi-explicit index $ 2$ differential-algebraic equations (DAEs) by methods based on Runge-Kutta (RK) coefficients. For nonstiffly accurate RK coefficients, such as Gauss and Radau IA coefficients, the standard application of implicit RK methods is generally not superconvergent. To reestablish superconvergence projected RK methods and partitioned RK methods have been proposed. In this paper we propose a simple alternative which does not require any extra projection step and does not use any additional internal stage. Moreover, symmetry of Gauss methods is preserved. The main idea is to replace the satisfaction of the constraints at the internal stages in the standard definition by enforcing specific linear combinations of the constraints at the numerical solution and at the internal stages to vanish. We call these methods specialized Runge-Kutta methods for index $ 2$ DAEs (SRK-DAE$ 2$).


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Additional Information

Laurent O. Jay
Affiliation: Department of Mathematics, 14 MacLean Hall, The University of Iowa, Iowa City, Iowa 52242-1419
Email: ljay@math.uiowa.edu E-mail address: na.ljay@na-net.ornl.gov

DOI: https://doi.org/10.1090/S0025-5718-05-01809-0
Keywords: Differential-algebraic equations, index $2$, Runge-Kutta methods
Received by editor(s): January 15, 2004
Received by editor(s) in revised form: January 26, 2005
Published electronically: December 19, 2005
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. 9983708.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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