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  • Articles  (9)
  • AMS(MOS)  (9)
  • 1975-1979  (9)
  • 1945-1949
  • 1979  (9)
  • Mathematics  (9)
  • Sociology
  • Architecture, Civil Engineering, Surveying
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  • Articles  (9)
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  • 1975-1979  (9)
  • 1945-1949
Year
  • 1979  (9)
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  • Mathematics  (9)
  • Sociology
  • Architecture, Civil Engineering, Surveying
  • 1
    Electronic Resource
    Electronic Resource
    The method of lines for nonlinear parabolic differential equations with mixed derivatives (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 197-207 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65 M 20 ; CR 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary By the so-called longitudinal method of lines the first boundary value problem for a parabolic differential equation is transformed into an initial value problem for a system of ordinary differential equations. In this paper, for a wide class of nonlinear parabolic differential equations the spatial derivatives occuring in the original problem are replaced by suitable differences such that monotonicity methods become applicable. A convergence theorem is proved. Special interest is devoted to the equationu t=f(x,t,u,u x,u xx), if the matrix of first order derivatives off(x,t,z,p,r) with respect tor may be estimated by a suitable Minkowski matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404875
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  • 2
    Electronic Resource
    Electronic Resource
    Unconditionally stable methods for second order differential equations (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 373-379 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65L05 ; CR ; 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We use the concept of order stars (see [1]) to prove and generalize a recent result of Dahlquist [2] on unconditionally stable linear multistep methods for second order differential equations. Furthermore a result of Lambert-Watson [3] is generalized to the multistage case. Finally we present unconditionally stable Nyström methods of order 2s (s=1,2, ...) and an unconditionally stable modification of Numerov's method. The starting point of this paper was a discussion with G. Wanner and S.P. Nørsett. The author is very grateful to them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401041
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  • 3
    Electronic Resource
    Electronic Resource
    New extremal properties for constructing conformal mappings (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 423-429 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 30A28 ; 30A38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary It is well known that for a given simply connected regionR containing zero the uniform norm $$\left\| f \right\| = \mathop {\sup }\limits_{z \in R} \left| {f(z)} \right|$$ attains its minimum in the class of all holomorphic functions normalized byf(0)=0 andf′(0)=1 only for the conformal mappingf∶R→D(r)={z∶|z|〈r}. It is shown that this theorem is still valid if one replaces the ordinary modulus | | on ℂ by any other norm on ℂ. For instance it is possible to obtain direct mappings ofR onto parallelograms, rectangles and ellipses. For the special norms |1 and |∞ this leads to a simple and fast computational technique involving linear programming methods. Several numerical examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401045
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  • 4
    Electronic Resource
    Electronic Resource
    An algorithm for the zeros of transcendental functions (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 359-371 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65H05 R ; 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we extend the dual form of the generalized algorithm of Sebastião e Silva [3] for polynomial zeros and show that it is effective for finding zeros of transcendental functions in a circle of analyticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401040
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  • 5
    Electronic Resource
    Electronic Resource
    On the inversion of the attenuated Radon transform (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 431-438 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65R05 ; CR ; 5.18
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We given an inversion formula for the attenuated Radon transform $$\bar \omega _L $$ for constant attenuation μ which is accurate up toO(µ 4) We also derive an integral equation of the second kind for the solution ofR μf=g. The implementation of both methods for the inversion ofR μ consists basically of a generalized filtered backprojection algorithm. Numerical examples are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401046
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  • 6
    Electronic Resource
    Electronic Resource
    A 0-Stability and stiff stability of Brown's multistep multiderivative methods (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 167-181 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Brown [1] introducedk-step methods usingl derivatives. Necessary and sufficient conditions forA 0-stability and stiff stability of these methods are given. These conditions are used to investigate for whichk andl the methods areA 0-stable. It is seen that for allk andl withk≦1.5 (l+1) the methods areA 0-stable and stiffly stable. This result is conservative and can be improved forl sufficiently large. For smallk andl A 0-stability has been determined numerically by implementing the necessary and sufficient condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404873
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  • 7
    Electronic Resource
    Electronic Resource
    La méthode de Kikuchi appliquée aux équations de von Karman (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 209-232 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Resumé Le but de cet article est l'étude de l'approximation numérique des solutions non-triviales des équations de Von Karman pour le flambage d'une plaque mince encastrée. S'inspirant de la méthode de Kikuchi pour des problèmes quasi-linéaires du second ordre, on propose une méthode itérative d'éléments finis qui donne des approximations des solutions de norme «petite» qui bifurquent de la solution triviale au voisinage d'une valeur propre simple du problème linéarisé. On démontre la convergence et on obtient des estimations de l'erreur.
    Notes: Summary The aim of this article is to study the numerical approximation of non-trivial solutions of the Von Karman equations for the buckling of a thin elastic clamped plate. Following Kikuchi's method for second order quasilinear problems, we propose an iterative finite element method which produces approximations of non-trivial solutions of “small” norm which bifurcate from the trivial solution near simple eigenvalues of the linearised problem. The convergence is proved and error estimates are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01404876
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  • 8
    Electronic Resource
    Electronic Resource
    Pointwise inclusions of fixed points by finite dimensional iteration schemes (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 381-392 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65R05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Finite dimensional iteration schemes which provide pointwise bounds for the solutions of nonlinear integral equations are considered. The method is based on a discretization technique which takes advantage of apriori known structure properties of the solutions. The resulting iteration can be carried out on a computer for as many steps as desired. Its high degree of accuracy is shown by numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401042
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  • 9
    Electronic Resource
    Electronic Resource
    The general recurrence relation for divided differences and the general Newton-interpolation-algorithm with applications to trigonometric interpolation (1979)
    Springer
    Numerische Mathematik 32 (1979), S. 393-408 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65D05 ; 41A05 ; 42A12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this note an ultimate generalization of Newton's classical interpolation formula is given. More precisely, we will establish the most general linear form of a Newton-like interpolation formula and a general recurrence relation for divided differences which are applicable whenever a function is to be interpolated by means of linear combinations of functions forming a Čebyšev-system such that at least one of its subsystems is again a Čebyšev-system. The theory is applied to trigonometric interpolation yielding a new algorithm which computes the interpolating trigonometric polynomial of smallest degree for any distribution of the knots by recurrence. A numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01401043
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