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Numerical conformal mapping of multiply connected regions by Fornberg-like methods

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Summary.

We develop a new algorithm for computing conformal maps from regions exterior to non-overlapping disks to unbounded multiply connected regions exterior to non-overlapping, smoothly bounded Jordan regions. The method is an extension of Fornberg's original Newton-like method for mapping of the disk to simply connected regions. A Fortran program based on the algorithm has been developed and tested for the 2 and 3 disk case. Numerical examples are reported.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260–0033, USA; e-mail: delillo@twsuvm.uc.twsu.edu , , , , , , US

    Thomas K. DeLillo

  2. ARINC, Inc., 6703 Odyssey Drive, Suite 104, Huntsville, AL 35806, USA; e-mail: mhorn@arinc.com , , , , , , US

    Mark A. Horn

  3. Department of Mathematics, University of North Carolina at Chapel Hill, Phillips Hall, CB 3250, Chapel Hill, NC 27599-3250, USA; e-mail: jap@math.unc.edu , , , , , , US

    John A. Pfaltzgraff

Authors
  1. Thomas K. DeLillo
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  2. Mark A. Horn
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  3. John A. Pfaltzgraff
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Received March 12, 1998 / Revised version received December 16, 1998

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DeLillo, T., Horn, M. & Pfaltzgraff, J. Numerical conformal mapping of multiply connected regions by Fornberg-like methods. Numer. Math. 83, 205–230 (1999). https://doi.org/10.1007/s002110050447

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  • DOI: https://doi.org/10.1007/s002110050447

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