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  • CR: G1.7  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    An algebraic characterization ofB-convergent Runge-Kutta methods (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 695-705 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01405197
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    B-Convergence of Lobatto IIIC formulas (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 229-235 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A completion ofB-convergence results of Lobatto IIIC schemes is presented. In particular, it is shown that Lobatto IIIC schemes with more than two stages areB-convergent when applied to IVPs with a negative one-sided Lipschitz constantm; they are notB-convergent, however, for IVPs with a non-negativem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396751
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    Paper (German National Licenses)
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