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Numerical Methods for the Discrete Map $$Z^a$$ Z a

In: Advances in Discrete Differential Geometry

Author

Listed:
  • Folkmar Bornemann

    (Technische Universität München, Zentrum Mathematik – M3)

  • Alexander Its

    (Indiana University–Purdue University, Department of Mathematical Sciences)

  • Sheehan Olver

    (The University of Sydney, School of Mathematics and Statistics)

  • Georg Wechslberger

    (Technische Universität München, Zentrum Mathematik – M3)

Abstract

As a basic example in nonlinear theories of discrete complex analysis, we explore various numerical methods for the accurate evaluation of the discrete map $$Z^a$$ Z a introduced by Agafonov and Bobenko. The methods are based either on a discrete Painlevé equation or on the Riemann–Hilbert method. In the latter case, the underlying structure of a triangular Riemann–Hilbert problem with a non-triangular solution requires special care in the numerical approach. Complexity and numerical stability are discussed, the results are illustrated by numerical examples.

Suggested Citation

  • Folkmar Bornemann & Alexander Its & Sheehan Olver & Georg Wechslberger, 2016. "Numerical Methods for the Discrete Map $$Z^a$$ Z a," Springer Books, in: Alexander I. Bobenko (ed.), Advances in Discrete Differential Geometry, pages 151-176, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-50447-5_4
    DOI: 10.1007/978-3-662-50447-5_4
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