Schwarz—Christoffel Integrals

Prem K. Kythe
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Prem K. Kythe: University of New Orleans, Department of Mathematics

Chapter Chapter 3 in Computational Conformal Mapping, 1998, pp 68-91 from Springer

Abstract: Abstract In practical applications of conformal mapping of a standard region (the half—plane or the unit disk) onto a problem region which is in the form of a polygon, it becomes necessary to determine approximately the (2n + 2) parameters al,…, an, x1,…, x n , and the constants A and B that appear in the Schwarz—Christoffel formula (2.3.1). Evaluation of these quantities is known as the parameter problem. We have seen in case studies in §2.3 that the mapping functions obtained by using the Schwarz—Christoffel formula involve certain improper integrals which are known as Schwarz—Christoffel integrals. We shall discuss methods for numerical solution of these integrals and present Newton’s method for the general case of mapping the upper half—plane onto a quadrilateral.

Date: 1998
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DOI: 10.1007/978-1-4612-2002-2_4

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