Abstract
Methods are called A -stable if there are no stability restrictions for y′ = λy, Re λ < 0 and h > 0. This concept was introduced by Dahlquist (1963) for linear multistep methods, but also applied to Runge-Kutta processes. Ehle (1968) and Axelsson (1969) then independently investigated the A -stability of implicit Runge-Kutta methods and proposed new classes of A -stable methods. A nice paper of Wright (1970) studied collocation methods.
I didn’t like all these “strong”, “perfect”, “absolute”, “generalized”, “super” “hyper”, “complete” and so on in mathematical definitions, I wanted something neutral; and having been impressed by David Young’s “property A”, I chose the term “A-stable”.
(G. Dahlquist, in 1979)
There are at least two ways to combat stiffness. One is to design a better computer, the other, to design a better algorithm.
(H. Lomax in Aiken 1985)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hairer, E., Wanner, G. (1996). Stability Function of Implicit RK-Methods. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-05221-7_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05220-0
Online ISBN: 978-3-642-05221-7
eBook Packages: Springer Book Archive