 Theodorsen’s Integral EquationPrem K. Kythe
Chapter Chapter 8 in Computational Conformal Mapping, 1998, pp 207-236 from Springer Abstract: Abstract The problem of conformally mapping an almost circular region onto the interior or exterior of a circular disk by the the method of infinite systems was discussed in Chapter 5. In this chapter we shall present Theodorsen’s integral equation and establish the convergence of the related iterative method for the standard case of mapping the unit circle onto the interior (or exterior) of almost circular and starlike regions, both containing the origin. A trigonometric interpolation scheme is presented, and Wegmann’s iterative and Newton’s method for numerically solving this equation are discussed. The last two methods are based on a certain Riemann—Hilbert problem, which turns out to be a linearized form of a singular integral equation of the second kind. Unlike the classical iterative method, the solution of the linearized problem in Wegmann’s method for the conformal map of the unit circle can be represented explicitly in terms of integral transforms, which leads to a quadratic convergent Newton—like method that avoids the numerical solution of a system of linear equations and thus becomes more economical. Theodorsen’s integral equation has specific significance in the theory of airfoils. Date: 1998 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2002-2_9 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4612-2002-2_9 Access Statistics for this chapter More chapters in Springer Books from Springer |
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