Numerical Methods for the Discrete Map $Z^a$

Folkmar Bornemann; Alexander Its; Sheehan Olver; Georg Wechslberger

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arXiv · 1507.06805

Numerical Methods for the Discrete Map $Z^a$

Folkmar Bornemann·Alexander Its·Sheehan Olver·Georg Wechslberger

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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 $Z^a$ 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

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Folkmar Bornemann, Alexander Its, Sheehan Olver, Georg Wechslberger. 2015-08-23. Numerical Methods for the Discrete Map $Z^a$. https://arxiv.org/abs/1507.06805

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