ISSN:
1572-9125
Keywords:
65L05
;
65L20
;
65D07
;
Ordinary differential equations
;
collocation methods
;
A-stability
;
confluence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper the general classV of spline-collocation methods presented by Mülthei is investigated. The methods ofV approximate solutions of first order initial value problems. ClassV contains as subclass the methods of so-called multivalue type, and in particular contains the generalized singly-implicit methods treated by Butcher. Any multivalue type representativeU εV yields a matrix valued function Ω corresponding toU, which characterizes the region of absolute stability ofU. If a sequence (U(δ)) of multivalue type representatives ofV tending to some singlevalue type representative $$\tilde U$$ εV is considered, it can easily be seen by the structure of Ω, that the sequence of the greatest eigenvalues of the Ω(.,δ) tends to the stability function $$\tilde R$$ corresponding to $$\tilde U$$ . This fact allows one to construct one-parameter families of A-stable methods of multivalue type.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01952684
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