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  • 1
    Electronic Resource
    Electronic Resource
    Monotone iteration discretization algorithm for BVP's (1989)
    Springer
    Computing 41 (1989), S. 59-74 
    Details
    ISSN: 1436-5057
    Keywords: 65L10 ; Boundary value problem ; monotone iteration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit wird eine neue Diskretisierungstechnik zur Erzeugung von Lösungseinschließungen bei schwach nichtlinearen 2-Punkt-Randwertaufgaben vorgeschlagen. Mittels verfügbarer Abschätzungen werden Unter-und Oberlösungen erzeugt. Die Monotonie des Verfahrens wird durch Prinzipien der monotonen Iteration gesichert. Es werden die Konvergenzeigenschaften des vorgeschlagenen Verfahrens analysiert.
    Notes: Abstract In this paper we propose a new discretization technique generating enclosures of the solution of a weakly nonlinear 2-point boundary value problem. By means of available extimations lower and upper solutions are generated. The monotonicity of the method is guaranteed by principles of monotone iterations. The convergence properties of the proposed algorithm are analyzed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238729
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Directional approximation of the jacobians in ROW-methods (1991)
    Springer
    BIT 31 (1991), S. 89-101 
    Details
    ISSN: 1572-9125
    Keywords: 65L05 ; Numerical analysis ; stiff problems ; Rosenbrock methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper a new technique for avoiding exact Jacobians in ROW methods is proposed. The Jacobiansf' n are substituted by matricesA n satisfying a directional consistency conditionA n f n =f' n f n +O(h). In contrast to generalW-methods this enables us to reduce the number of order conditions and we construct a 2-stage method of order 3 and families of imbedded 4-stage methods of order 4(3). The directional approximation of the Jacobians has been realized via rank-1 updating as known from quasi-Newton methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01952786
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    An effective method for solving linear programming problems with flexible constraints (1983)
    Springer
    Mathematical methods of operations research 27 (1983), S. 107-122 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Für lineare Optimierungsprobleme mit flexiblen Restriktionen, die spezielle stückweise lineare Programme darstellen, wird ein neues Lösungsverfahren auf der Grundlage einer systematischen Zerlegung des zulässigen Bereiches in Linearitätsbereiche vorgeschlagen und dessen Konvergenz nachgewiesen.
    Notes: Abstract For solving linear programming problems with flexible constraints being specific piecewise linear programs a new algorithm which is based on a systematic decomposition of the feasible set into linear constrained subsets is proposed and shown to converge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01916905
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    Paper (German National Licenses)
    Fulltext
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