Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    On the numerical solution of Cauchy type singular integral equations and the determination of stress intensity factors in case of complex singularities (1977)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 28 (1977), S. 1085-1098 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Une équation intégrale du type de Cauchy singulière le long d'un intervalle fini réel et avec une fonction pondérante ayant des singularités complexes aux extremités de l'intervalle d'intégration peut être résolue numériquement par réduction à un système d'équations linéaires, en utilisant une règle appropriée d'intégration numérique associée aux polynômes de Jacobi, exactement de la même manière que dans le cas des singularités réelles. La façon la plus appropriée de trouver la solution numérique de cette équation telle qu'elle se présente dans les problèmes de fissure en élasticité plane et d'évaluer les facteurs de contrainte aux extremités da la fissure est la méthode d'intégration numérique de Lobatto-Jacobi.
    Notes: Summary A Cauchy type singular integral equation along a finite real interval and with a weight function with complex singularities at the end-points of the integration interval can be numerically solved by reduction to a system of linear equations, by using an appropriate numerical integration rule associated with the Jacobi polynomials, in exactly the same way used for the case of real singularities. For the numerical solution of such an equation arising in plane elasticity crack problems and the evaluation of stress intensity factors at crack tips, the Lobatto-Jacobi numerical integration rule is the most appropriate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01601675
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Application of the Cauchy theorem to the location of zeros of sectionally analytic functions (1984)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 35 (1984), S. 705-711 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Une nouvelle méthode pour la dérivation de formules analytiques pour les zéros des fonctions analytiques par morceaux dans le plan complexe est proposée. Cette méthode se base sur le théorème de Cauchy dans l'analyse complexe (sous une forme généralisée) et elle n'a besoin de la solution d'aucun problème à valeurs aux limites le long de l'intervalle de discontinuité. Comme une application, l'équation transcendentale classiquew=tanh (p w+q), apparaissante dans un problème physique, est résolue analytiquement. Des résultats numériques sont présentées aussi.
    Notes: Summary A new method for the derivation of closed-form formulae for the zeros of sectionally analytic functions in the complex plane is proposed. This method is based on the Cauchy theorem in complex analysis (in a generalized form) and it does not require the solution of any boundary value problem along the discontinuity interval. As an application, the classical transcendental equationw=tanh (p w+q), appearing in a physical problem, is solved in closed form. Numerical results are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00952115
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Application of the generalized Siewert-Burniston method to locating zeros and poles of meromorphic functions (1985)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 733-742 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé La méthode de Siewert et Burniston généralisée pour la détermination des zéros d'une fonction analytique à l'intérieur d'un contourC simple fermé dans le plan complexe est modifiée pour être applicable à la détermination des zéros ainsi que des pôles d'une fonction méromorphe à l'intérieur deC. La méthode se base encore une fois à la résolution d'un problème de valeurs aux limites de Riemann-Hilbert surC; les valeurs de la fonction méromorphe surC étant suffisantes pour l'application de la méthode.
    Notes: Summary The generalized Siewert-Burniston method for the determination of the zeros of an analytic function inside a simple closed contourC in the complex plane is modified to be applicable to the determination of both the zeros and the poles of a meromorphic function insideC. The method is based again on the solution of a homogeneous Riemann-Hilbert boundary value problem onC and the values of the meromorphic function onC are sufficient for the application of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00960384
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    On the simultaneous determination of zeros of analytic or sectionally analytic functions (1986)
    Springer
    Computing 36 (1986), S. 239-247 
    Details
    ISSN: 1436-5057
    Keywords: Primary ; 65H05 ; secondary ; 30C15 ; 30E20 ; Analytic functions ; polynomials ; Riemann-Hilbert boundary value problem ; sectionally analytic functions ; simultaneous iterative methods ; single-step method ; zeros
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, wie die Totalschritt- und Einschritt-Iterations-Verfahren für die gleichzeitige Bestimmung von einfachen Nullstellen von Polynomen sowie ihre Verbesserungen (mit einer kleinen Modifikation) für die Bestimmung von einfachen Nullstellen analytischer Funktionen (im inneren oder äußeren einer einfachen glatten abgeschlossenen Kontur in der komplexen Ebene) oder stückweise analytischer Funktionen (im äußeren ihrer Unstetigkeitsbögen) benutzt werden können. Numerische Ergebnisse, die mit der Einschrittmethode erhalten wurden, werden auch präsentiert.
    Notes: Abstract It is shown how the total-step and single-step iterative methods, as well as their improvements, for the simultaneous determination of simple zeros of polynomials can be used (with one slight modification) for the determination of simple zeros of analytic functions (inside or outside a simple smooth closed contour in the complex plane) or sectionally analytic functions (outside their arcs of discontinuity). Numerical results, obtained by the single-step method, are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240070
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    A new method for obtaining exact analytical formulae for the roots of transcendental functions (1984)
    Springer
    Letters in mathematical physics 8 (1984), S. 135-143 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A new method is proposed for the derivation of closed-form formulae for the zeros and poles of sectionally analytic functions in the complex plane. This method makes use of the solution of the simple discontinuity problem in the theory of analytic functions and requires the evaluation of real integrals only (for functions with discontinuity intervals along the real axis). Many transcendental equations of mathematical physics can be successfully solved by the present approach. An application to such an equation, the molecular field equation in the theory of ferromagnetism, is made and the corresponding analytical formulae are reported together with numerical results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00406396
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    An elementary noniterative quadrature-type method for the numerical solution of a nonlinear equation (1986)
    Springer
    Computing 37 (1986), S. 269-275 
    Details
    ISSN: 1436-5057
    Keywords: Primary 65H05 ; secondary: 65D32 ; Cauchy-type principal value integrals ; convergence ; Gauss- and Lobatto-Chebyshev quadrature rules ; nonlinear equations ; numerical integration ; roots ; transcendental equations ; zeros
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wurde eine einfache nicht-iterative Methode für die numerische Berechnung einer einfachen Nullstelle einer nichtlinearen differenzierbaren algebraischen oder transzendenten Funktion längs eines endlichen reellen Intervalles vorgestellt. Die Methode gründet sich auf die Berechnung eines Integrales, das die Funktion enthält, mittels der Gauß- und der Lobatto-Tschebyscheff-Quadraturformeln und die anschließende gleichsetzung der erhaltenen Resultate. Die Konvergenz der Methode wird unter schwachen Annahmen bewiesen; numerische Resultate sind für zwei klassiche transzendente Gleichungen angegeben.
    Notes: Abstract A simple noniterative method for the numerical determination of one simple root of a nonlinear differentiable algebraic or transcendental function along a finite real interval is proposed. This method is based on the computation of an integral involving the above function both by the Gauss- and the Lobatto-Chebyshev quadrature rules for regular integrals and equating the obtained results. The convergence of the method is proved under mild assumptions and numerical results for two classical transcendental equations are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02252519
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    On the natural interpolation formula for cauchy type singular integral equations of the first kind (1981)
    Springer
    Computing 26 (1981), S. 73-77 
    Details
    ISSN: 1436-5057
    Keywords: Cauchy type singular integral equations ; natural interpolation formulae ; Gauss-Chebyshev quadrature rule ; Nyström (quadrature) method for integral equations ; direct numerical solution of Cauchy type singular integral equations ; Primary: 65R20 ; Secondary: 45E05, 45L10, 65D05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eine singuläre Integralgleichung erster Art vom Cauchy-Typ kann entweder direkt, mittels einer Gaußschen numerischen Integrationsformel, oder durch Reduktion auf eine äquivalente Fredholmsche Integralgleichung zweiter Art, wo die Nyström-Methode anwendbar ist, gelöst werden. In dieser Arbeit wird bewiesen, daß unter geeigneten und sinnvollen Bedingungen die Ausdrücke der unbekannten Funktion der Integralgleichung, die einerseits bei den natürlichen Integrationsformeln der direkten Methode und anderseits bei der Nyström-Methode entstehen, im ganzen Integrationsintervall gleich sind.
    Notes: Abstract A Cauchy type singular integral equation of the first kind can be numerically solved either directly, through the use of a Gaussian numerical integration rule, or by reduction to an equivalent Fredholm integral equation of the second kind, where the Nyström method is applicable. In this note it is proved that under appropriate but reasonable conditions the expressions of the unknown function of the integral equation, resulting from the natural interpolation formulae of the direct method, as well as of the Nyström method, are identical along the whole integration interval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243425
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    On convergence of two direct methods for solution of Cauchy type singular integral equations of the first kind (1980)
    Springer
    BIT 20 (1980), S. 83-87 
    Details
    ISSN: 1572-9125
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The methods for direct numerical solution of Cauchy type singular integral equations of the first kind based on Gauss-Chebyshev or Lobatto-Chebyshev numerical integration and the reduction of such an integral equation to a system of linear equations are proved to converge under appropriate conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933588
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    A new simple method for the analytical solution of Kepler's equation (1985)
    Springer
    Celestial mechanics and dynamical astronomy 35 (1985), S. 305-316 
    Details
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new simple method for the closed-form solution of nonlinear algebraic and transcendental equations through integral formulae is proposed. This method is applied to the solution of the famous Kepler equation in the two-body problem for elliptic orbits. The resulting formulae are quite elementary and, beyond their analytical interest, they can also provide quite accurate numerical results by using Gausstype quadrature rules.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01227827
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Numerical evaluation of analytic functions by Cauchy's theorem (1991)
    Springer
    BIT 31 (1991), S. 276-285 
    Details
    ISSN: 1572-9125
    Keywords: primary: 65E05 ; secondary: 30E20, 65D32 ; analytic functions ; asymptotic estimates ; Cauchy formula ; Cauchy theorem ; circle ; contour ; complex contour integrals ; error bounds ; error term ; numerical integration ; Taylor series ; trapezoidal quadrature rule
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The use of the Cauchy theorem (instead of the Cauchy formula) in complex analysis together with numerical integration rules is proposed for the computation of analytic functions and their derivatives inside a closed contour from boundary data for the analytic function only. This approach permits a dramatical increase of the accuracy of the numerical results for points near the contour. Several theoretical results about this method are proved. Related numerical results are also displayed. The present method together with the trapezoidal quadrature rule on a circular contour is investigated from a theoretical point of view (including error bounds and corresponding asymptotic estimates), compared with the numerically competitive Lyness-Delves method and rederived by using the Theotokoglou results on the error term. Generalizations for the present method are suggested in brief.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01931287
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...