Abstract
Prothero & Robinson (1974) were the first to discover the order reduction of implicit Runge-Kutta methods when applied to stiff differential equations. Frank, Schneid & Ueberhuber (1981) then introduced the “concept of B -convergence”, which furnishes global error estimates independent of the stiffness.
In using A -stable one-step methods to solve large systems of stiff nonlinear differential equations, we have found that
— (a) some A -stable methods give highly unstable solutions, and
— (b) the accuracy of the solutions obtained when the equations are stiff often appears to be unrelated to the order of the method used.
This has caused us to re-examine the form of stability required when stiff systems of equations are solved, and to question the relevance of the concept of (nonstiff) order of accuracy for stiff problems.
(A. Prothero & A. Robinson 1974)
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© 1996 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G. (1996). B-Convergence. In: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7_15
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DOI: https://doi.org/10.1007/978-3-642-05221-7_15
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