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On the simultaneous determination of zeros of analytic or sectionally analytic functions (1986)

Ioakimidis, N. I. ; Anastasselou, E. G.

Springer

Computing 36 (1986), S. 239-247

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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

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A natural interpolation formula for Prandtl's singular integrodifferential equation (1984)

Ioakimidis, N. I.

Chichester : Wiley-Blackwell

International Journal for Numerical Methods in Fluids 4 (1984), S. 283-290

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ISSN: 0271-2091

Keywords: Prandtl's Equation ; Singular Integrodifferential Equations ; Quadrature Method ; Natural Interpolation Formula ; Principal Value Integrals ; Gauss- and Lobatto-Chebyshev Quadrature Rules ; Engineering ; Engineering General

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics

Notes: Prandtl's singular integrodifferential equation and related equations appear in problems of aerofoil and propeller theory in fluid mechanics. Here a natural interpolation formula for the approximation to the unknwon function of Prandtl's equation when this is solved numerically by the direct quadrature method, based on the Gauss- and Lobatto-Chebyshev quadrature rules, is proposed. This interpolation formula is analogous to Nyström's natural interpolation formula for Fredholm integral equations of the second kind and the corresponding formula for singular integral equations. Numerical applications of the same formula are also made.

Additional Material: 2 Tab.