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  • 1
    Digitale Medien
    Digitale Medien
    A generalization of singly-implicit methods (1981)
    Springer
    BIT 21 (1981), S. 175-189 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 5.17 ; 65L05
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Singly-implicit Runge-Kutta methods are characterized by a one-point spectrum property of the coefficient matrix. If a method of this type is also a collocation method, then its abscissae are proportional to the zeros of a Laguerre polynomial. The generalization introduced here is a multistep method in the style of Nordsieck and also a multistage method under the one-point spectrum constraint. It is found that much of the theory of singly-implicit methods carries over but with Laguerre polynomials replaced by their usual generalizations. Amongst the formal properties of the new method which are studied is a derivation of the similarity transformations which allow their efficient implementation. A preliminary investigation is made of the stability of the new methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01933162
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Linear and non-linear stability for general linear methods (1987)
    Springer
    BIT 27 (1987), S. 181-189 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 65L20 ; 5.17
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We explore the interrelation between a number of linear and non-linear stability properties. The weakest of these,A-stability, is shown by counterexample not to imply any of the various versions ofAN-stability introduced in the paper and two of these properties, weak and strongAN-stability, are also shown not to be equivalent. Finally, another linear stability property defined here, EuclideanAN-stability, is shown to be equivalent to algebraic stability.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01934183
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    The equivalence of algebraic stability andAN-stability (1987)
    Springer
    BIT 27 (1987), S. 510-533 
    Details
    ISSN: 1572-9125
    Schlagwort(e): 5.17 ; 65L20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is shown that, under certain restrictions,AN-stability is equivalent to algebraic stability for general linear methods. The restrictions have the purpose of excluding from consideration methods which can be replaced by simpler methods in various specific ways andAN-stability is to be interpreted in the strong sense. This result generalizes known results for Runge-Kutta and for one-leg methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01937275
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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