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Numerical computation of a preimage domain for an infinite strip with rectilinear slits

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Abstract

Let Ω be the multiply connected domain in the extended complex plane \(\overline {\mathbb {C}}\) obtained by removing m non-overlapping rectilinear segments from the infinite strip \(S=\{z : \left |\text {Im} z\right |<\pi /2\}\). In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply connected domain G in the interior of the unit disk \(\mathbb {D}\) and the exterior of m non-overlapping smooth Jordan curves. We demonstrate the utility of the proposed method through two applications. First, we estimate the capacity of condensers of the form (S,E) where E ⊂ S is a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip S.

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Acknowledgements

We are indebted to Prof. A. Yu. Solynin and Prof. D. Betsakos who have independently provided an analytic argument to confirm our experimental discovery (3) and Example 7. We would also like to thank two anonymous reviewers for their valuable comments and for bringing several bibliographic items to our attention.

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Authors and Affiliations

  1. School of Science and Engineering, Al Akhawayn University in Ifrane, PO Box 104, Ifrane, 53000, Morocco

    El Mostafa Kalmoun

  2. Department of Mathematics, Statistics & Physics, Wichita State University, Wichita, KS, 67260-0033, USA

    Mohamed M. S. Nasser

  3. Department of Mathematics and Statistics, University of Turku, FI-20014, Turku, Finland

    Matti Vuorinen

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  1. El Mostafa Kalmoun
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  2. Mohamed M. S. Nasser
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  3. Matti Vuorinen
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Correspondence to Mohamed M. S. Nasser.

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Communicated by: Silas Alben

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Kalmoun, E.M., Nasser, M.M.S. & Vuorinen, M. Numerical computation of a preimage domain for an infinite strip with rectilinear slits. Adv Comput Math 49, 5 (2023). https://doi.org/10.1007/s10444-022-10006-y

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