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  • AMS (MOS): 65L05  (1)
  • AMS(MOS): 65Q05  (1)
  • watchdog strategy  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On improving the absolute stability of local extrapolation (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 329-337 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396450
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A note on the numerical solution of linear recurrence relations (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 371-386 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65Q05 ; CR: 5.11, 5.12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A numerical algorithm for the computation of non-dominant solutions of linear recurrence relations is analysed. Several non-trivial improvements are made and the efficiency of the new algorithm is illustrated by means of some numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403675
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Implementation issues in solving nonlinear equations for two-point boundary value problems (1990)
    Springer
    Computing 45 (1990), S. 17-37 
    Details
    ISSN: 1436-5057
    Keywords: 65L10 (boundary value problems) ; 68N99 (mathematical software) ; Boundary value problems ; nonlinear algebraic equations ; merit functions ; mathematical software ; watchdog strategy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Komplizierte numerische Methoden enthalten oft Teilprobleme, die sich leicht mathematisch formulieren lassen, die aber schwierig in Computerprogramme umgewandelt werden können. Mehrere solche Fragestellungen traten bei der Erstellung eines Newton-Verfahrens als Bestandteil eines Differenzenverfahrens für 2-Punkt Randwert-probleme auf. Wir beschreiben die praktischen und theoretischen Überlegungen, welche den Entscheidungen zugrunde liegen, die schließlich zum Computerprogramm führten. Insbesondere betonen wir dabei zwei “Watchdog”-Strategien, welche die Zuverlässigkeit verbessern und ein frühes Abbrechen der Newton-Iteration ermöglichen.
    Notes: Abstract Complex numerical methods often contain subproblems that are easy to state in mathematical form, but difficult to translate into software. Several algorithmic isues of this nature arise in implementing a Newton iteration scheme as part of a finite-difference method for two-point boundary value problems. We describe the practical as well as theoretical considerations behind the decisions included in the final code, with special emphasis on two “watchdog” strategies designed to improve reliability and allow early termination of the Newton iterates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02250582
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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