Algebraic stability and the existence of solutions of implicit Runge-Kutta equations
Author:
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computer Networks and Communications,Software
Link
http://link.springer.com/content/pdf/10.1007/BF01934382.pdf
Reference7 articles.
1. K. Burrage and J. C. Butcher,Stability criteria for implicit Runge-Kutta methods, SIAM J. Numer. Anal. 16 (1979), 46–57.
2. K. Burrage and J. C. Butcher,Non-linear stability of a general class of differential equation methods, BIT 20 (1980), 185–203.
3. G. J. Cooper,A generalization of algebraic stability for Runge-Kutta methods, IMA J. Numer. Anal. 4 (1984), 427–440.
4. M. Crouzeix,Sur la B-stabilité des méthodes de Runge-Kutta, Numer. Math. 32 (1979), 75–82.
5. M. Crouzeix, W. H. Hundsdorfer and M. N. Spijker,On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods, BIT 23 (1983), 84–91.
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1. Solvability of concatenated Runge–Kutta equations for second-order nonlinear PDEs;Journal of Computational and Applied Mathematics;2013-06
2. The existence and uniqueness of solutions for the nonlinear algebraic equations in implicit R-K methods;International Journal of Computer Mathematics;1995-01
3. The existence and uniqueness of solutions for the nonlinear algebraic equations in implicit r-k methods;International Journal of Computer Mathematics;1994-01
4. Error bounding functions for Runge-Kutta methods;Applied Numerical Mathematics;1989-02
5. On the Existence of Solutions for Algebraically Stable Runge—Kutta Methods;IMA Journal of Numerical Analysis;1986
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