Numerical Methods for the Discrete Map $Z^a$
Numerical Analysis
2015-08-25 v2 Complex Variables
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 introduced by Agafonov and Bobenko. The methods are based either on a discrete Painlev\'e 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
Cite
@article{arxiv.1507.06805,
title = {Numerical Methods for the Discrete Map $Z^a$},
author = {Folkmar Bornemann and Alexander Its and Sheehan Olver and Georg Wechslberger},
journal= {arXiv preprint arXiv:1507.06805},
year = {2015}
}
Comments
added references and a conclusion; 24 pages, 10 figures