\(A\)-stable spline-collocation methods of multivalue type (Q1122952)
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scientific article; zbMATH DE number 4108080
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(A\)-stable spline-collocation methods of multivalue type |
scientific article; zbMATH DE number 4108080 |
Statements
\(A\)-stable spline-collocation methods of multivalue type (English)
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1989
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To approximate solutions of first order initial value problems, \textit{H. N. Mülthei} [Numer. Math. 39, 449-463 (1982; Zbl 0528.65040)] has studied a general class V of spline-collocation methods. This class V contains as a subclass the methods of the so-called multivalue type, in particular the generalized singly-implicit Runge-Kutta methods, treated by \textit{J. C. Butcher} [BIT 21, 175-189 (1981; Zbl 0484.65048)]. For this subclass, there exist only few results regarding \(A\)-stability. In this paper the author constructs one-parameter families of \(A\)-stable multivalue type methods. Examples are given.
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spline-collocation methods
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singly-implicit Runge-Kutta methods
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\(A\)-stability
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\(A\)-stable methods
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multivalue type methods
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0.96871793
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0.91945434
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0.91890603
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0.89559686
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0.8922876
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0.8909591
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