Numerical methods for the discrete map Za

Folkmar Bornemann; Alexander Its; Sheehan Olver; Georg Wechslberger

doi:10.1007/978-3-662-50447-5_4

Numerical methods for the discrete map Z^a

Folkmar Bornemann, Alexander Its, Sheehan Olver, Georg Wechslberger

Chair of Scientific Computing

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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.

Original language	English
Title of host publication	Advances in Discrete Differential Geometry
Publisher	Springer Berlin Heidelberg
Pages	151-176
Number of pages	26
ISBN (Electronic)	9783662504475
ISBN (Print)	9783662504468
DOIs	https://doi.org/10.1007/978-3-662-50447-5_4
State	Published - 1 Jan 2016

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AB - As a basic example in nonlinear theories of discrete complex analysis, we explore various numerical methods for the accurate evaluation of the discrete map Za 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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Numerical methods for the discrete map Z^a

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