On the convergence of Runge–Kutta methods for stiff non linear differential equations |
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Authors: | M Calvo S Gonzalez–Pinto JI Montijano |
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Institution: | (1) Departamento Matemática Aplicada, Universidad de Zaragoza, E-50009 Zaragoza, Spain , ES;(2) Departamento Análisis Matemático, Universidad de La Laguna, E-38271 Tenerife, Spain , ES |
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Abstract: | Summary. This paper studies the convergence properties of general Runge–Kutta methods when applied to the numerical solution of a
special class of stiff non linear initial value problems. It is proved that under weaker assumptions on the coefficients of
a Runge–Kutta method than in the standard theory of B-convergence, it is possible to ensure the convergence of the method
for stiff non linear systems belonging to the above mentioned class. Thus, it is shown that some methods which are not algebraically
stable, like the Lobatto IIIA or A-stable SIRK methods, are convergent for the class of stiff problems under consideration.
Finally, some results on the existence and uniqueness of the Runge–Kutta solution are also presented.
Received November 18, 1996 / Revised version received October 6, 1997 |
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Keywords: | Mathematics Subject Classification (1991):65L05 65L06 |
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