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  • 1
    Electronic Resource
    Electronic Resource
    On symmetrizers for Gauss methods (1991)
    Springer
    Numerische Mathematik 60 (1991), S. 465-476 
    Details
    ISSN: 0945-3245
    Keywords: 65L05 ; 65L20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper the maximum attainable order of a special class of symmetrizers for Gauss methods is studied. In particular, it is shown that a symmetrizer of this type for thes-stage Gauss method can attain order 2s-1 only for 1 ≦s ≦ 3, and that these symmetrizers areL-stable. A classification of the maximum attainable order of symmetrizers for some higher stages is presented. AnL-stable symmetrizer is also shown to exist for each of the methods studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385731
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  • 2
    Electronic Resource
    Electronic Resource
    Linear and non-linear stability for general linear methods (1987)
    Springer
    BIT 27 (1987), S. 181-189 
    Details
    ISSN: 1572-9125
    Keywords: 65L20 ; 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01934183
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  • 3
    Electronic Resource
    Electronic Resource
    The equivalence of algebraic stability andAN-stability (1987)
    Springer
    BIT 27 (1987), S. 510-533 
    Details
    ISSN: 1572-9125
    Keywords: 5.17 ; 65L20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01937275
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