On the existence of solutions to the algebraic equations in implicit runge-kutta methods |
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| Authors: | M. Crouzeix W. H. Hundsdorfer M. N. Spijker |
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| Affiliation: | 1. U.E.R. Mathématiques et Informatique, Université de Rennes, Campus Rennes-Beaulieu, 35042, Rennes Cedex, France
2. Institute of Applied Mathematics and Computer Science, University of Leiden, Wassenaarseweg 80, Leiden, The Netherlands
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| Abstract: | This paper deals with the systems of algebraic equations arising in the application ofB-stable Runge-Kutta methods. It is shown that under natural assumptions such systems do not always have a solution. In addition, general sufficient conditions are presented under which such systems do have unique solutions. |
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