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  • 1
    Electronic Resource
    Electronic Resource
    Iterative solutions of nonlinear initial value differential equations in Chebyshev series using Lie series (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 1-13 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 34A45, 34A50, 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper Lie series are presented in Chebyshev form and applied to the iterative solution of initial value problems in differential equations. The resulting method, though algebraically complicated, is of theoretical interest as a generalisation of Taylor series methods and iterative Chebyshev methods. The theory of the method is discussed and the solutions of some simple scalar equations are analysed to illustrate the behaviour of the process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01463994
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A series method for solving nonlinear two-point boundary value problems (1980)
    Springer
    Numerische Mathematik 34 (1980), S. 87-98 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 34A50 ; 34B15 ; 65L10 ; CR: 5, 17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new method for solving nonlinear boundary value problems based on Taylor-type expansions generated by the use of Lie series is derived and applied to a set of test examples. A detailed discussion is given of the comparative performance of this method under various conditions. The method is of theoretical interest but is not applicable, in its present form, to real life problems; in particular, because of the algebraic complexity of the expressions involved, only scalar second order equations have been discussed, though in principle systems of equations could be similarly treated. A continuation procedure based on this method is suggested for future investigation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396052
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Metal-Clad Multilayer Waveguide: Circle-Chain Convergent Method and Two Perturbation Methods (1999)
    Springer
    International journal of infrared and millimeter waves 20 (1999), S. 1425-1440 
    Details
    ISSN: 1572-9559
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Computer modeling studies for the calculation of the propagation constants and attenuation coefficients of TE mode in an asymmetric metal/ dielectric/dielectric layers structure are presented. Two different perturbation methods, circle chain convergent method and Downhill method are used. The last two methods can be used easily for the waveguides consist of any number of layers with complex refractive index due to gain and loss. The developed programs were run on a personal computer and numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021739314903
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A Perturbation Method for Complex Root Finding of Nonlinear Electromagnetic Waves (1999)
    Springer
    International journal of infrared and millimeter waves 20 (1999), S. 1389-1402 
    Details
    ISSN: 1572-9559
    Keywords: Nonlinear TE waves ; Lossy waveguides ; Numerical and perturbations techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Aspects of the perturbation method are presented and implemented on the analytic function of the complex variable for the propagation of nonlinear electromagnetic surface guided by a thin film. The behavior of nonlinear TE waves guided by asymmetrical dielectric thin film, bounded by a generalizes nonlinear substrate with a permittivity of the form ɛ ∼ | E |δ is analyzed. The complex roots, which correspond to the propagation and attenuation coefficient are obtained and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021783029924
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    Paper (German National Licenses)
    Fulltext
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