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  • 1
    Electronic Resource
    Electronic Resource
    Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung ΔU + k2U = 0 (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 48-67 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we present new methods to solve the classical Dirichlet and Neumann problems for ΔU + k2U = 0. We prove that the solutions of this equation for a region S containing G restricted to G are dense in L2(∂G). Introducing a basis in the space of solutions for S we find a complete orthogonal system in L2(∂G) which can be used to solve the boundary value problems by means of approximation in the Hilbertspace norm. Regularity estimates lead to series expansions in G.The well-known basis systems obtained by separation of variables thus may be used for every regular region without the very special geometric restrictions. Another class of basis systems may be obtained in analogy to the Runge. theorems by considering types of singularity functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020106
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Die Lösung der Prae-Maxwellschen Gleichungen mit Hilfe vollständiger LösungssystemeUnserem verehrten Lehrer, Herrn Prof. Dr. C. Müller, zum 60. Geburtstag gewidmet (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 410-418 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with the Neumann problem of the pre-Maxwell partial differential equations for a vector field v defined in a region G ⊂ R3. We approximate its uniquely determined solution (integrability conditions assumed) uniformly on G by explicitly computable particular integrals and linear combinations of vector fields with a “fundamental” sequence of points .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020404
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Die lösung der maxwellschen gleichungen durch vollständige flächenfeldsysteme (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 40-54 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper deals with approximation theorems for the solution of Maxwell's equations governing the mathematical description of the propagation of electromagnetic waves.The well-known results ([10]) for the Helmholtz equation are generalized to Maxwell's equations: Systems of electric (resp. magnetic) dipoles are proved to span the space of all solutions of rot H + iωE = 0, rotE - iωH = 0, with n × E prescribed on the boundary. The same result holds for the “Mie-potentials”Which can be proved by a Lemma of Mie [6].Two numerical examples for the three-dimensional boundary value problems (field of a dipole, field of reflection) are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070103
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A constructive approximation theorem for the oblique derivative problem in potential theory (1981)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 3 (1981), S. 104-114 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The (exterior) oblique derivative problem of potential theory is considered where l is a C(1,λ)-vector field on a regular boundary ∂Ge in Euclidean space R3 and the direction l at any point of ∂Ge forms with the outside normal n an angle ∢ (l, n) satisfying cos ∢ (l, n) ≥ c 〉 0. An approximation of the uniquely determined solution is given by use of trial functions {Φn}n=0,1,… harmonic in some region containing Ge and suitable for numerical purpose (for instance: solid spherical harmonics, certain sequences of fundamental solutions). The system {l▽Φn+hΦn}n=0,1,… defined on ∂Ge is shown to be closed and complete in the pre-Hilbert space C(0,λ)(∂Ge) of λ-Hölder continuous functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670030108
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    Paper (German National Licenses)
    Fulltext
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