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

Folkmar Bornemann (), Alexander Its (), Sheehan Olver () and Georg Wechslberger ()
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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

A chapter in Advances in Discrete Differential Geometry, 2016, pp 151-176 from Springer

Abstract: 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.

Keywords: Riemann-Hilbert Problem; Bobenko; Discrete Complex Analysis; Doubly-infinite Matrix; Singular Integral Equations (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-662-50447-5_4

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