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  • 1
    Electronic Resource
    Electronic Resource
    Amsterdam : Elsevier
    Journal of Computational Physics 27 (1978), S. 256-271 
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Der Zweck dieser Arbeit ist eine Darstellung der Wirksamkeit der zweidimensionalen Laplace-Transformation als eine Methode für die Auflösung von zeitabhängigen, linearen, partiellen Differentialgleichungen mit verschiedenen zeitabhängigen Randbedingungen. Die Hauptergebnisse der zweidimensionalen Laplace-Transformationstheorie werden benutzt, zusammen mit einem wirksamen numerischen Umkehralgorithmus. Die Formulierung und numerische Resultate werden vorgestellt für eine Anzahl von Aufgaben, die auf halbunendlichen und endlichen räumlichen Gebieten bestimmt sind. Die modifizierte zweidimensionale Laplace-Transformation wird beschrieben für den Fall, wo die räumliche Variable auf ein endliches Intervall beschränkt ist.
    Notes: Abstract The purpose of this paper is to demonstrate the effectiveness of the double Laplace transform as a method for solving time-invariant linear partial differential equations with a variety of time-varying boundary conditions. The main results of double Laplace transform theory are utilized together with an efficient numerical inversion algorithm. The formulation and numerical solutions are presented for a number of problems defined on both a semi-infinite and a finite spatial domain. The modified double Laplace transform is developed with the spatial variable defined on a finite interval.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 19 (1976), S. 381-400 
    ISSN: 1573-2878
    Keywords: Variable metric methods ; optimization theorems ; Hilbert spaces ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with some of the most powerful methods of minimizing functionals on Hilbert space. It is established that certain classes of these methods are equivalent and their convergence is proved for certain nonquadratic functionals on a Hilbert space. A computational study of these methods applied to a control problem is also included with particular reference to the equivalence of methods mentioned above.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 21 (1977), S. 199-211 
    ISSN: 1573-2878
    Keywords: Variable-metric methods ; optimization theorems ; Hilbert spaces ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the Hilbert-space analogue of a result of Huang, that all the methods in the Huang class generate the same sequence of points when applied to a quadratic functional with exact linear searches, is established. The convergence of a class of direct prediction methods based on some work of Dixon is then proved, and these methods are then applied to some control problems. Their performance is found to be comparable with methods involving exact linear searches.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 22 (1977), S. 399-415 
    ISSN: 1573-2878
    Keywords: Variable-metric methods ; optimization theorems ; Hilbert spaces ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the convergence of variable-metric methods without line searches (direct prediction methods) applied to quadratic functionals on a Hilbert space is established. The methods are then applied to certain control problems with both free endpoints and fixed endpoints. Computational results are reported and compared with earlier results. The methods discussed here are found to compare favorably with earlier methods involving line searches and with other direct prediction quasi-Newton methods.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 2325-2346 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The advantages in formulation and use of semi-discretized approaches to the numerical solution of initial/boundary value problems are well known. The aim of this paper is to demonstrate that it is feasible to obtain accurate results even with a coarse spatial mesh. A method is developed which produces in a simple manner matrix representations for high-order central difference operators. Dirichlet, Neumann and mixed boundary conditions are considered, both homogeneous and non-homogeneous. It is shown in all cases that, for linear problems at least, there is no need to use a finer mesh than that dictated by the essential frequency content of the initial function data.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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