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On numerical algorithms for the solution of a Beltrami equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2008 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 46, no 5, 2238-2253 p.Article in journal (Refereed) Published
Abstract [en]

The paper concerns numerical algorithms for solving the Beltrami equation f (z) over bar (z) = mu( z) fz( z) for a compactly supported mu. First, we study an e. cient algorithm that has been proposed in [ P. Daripa, J. Comput. Phys., 106 ( 1993), pp. 355 - 365] and [ P. Daripa and D. Mashat, Numer. Algorithms, 18 ( 1998), pp. 133 - 157] and present its rigorous justi. cation. We then propose a different scheme for solving the Beltrami equation which has a comparable speed and accuracy, but has the virtue of easier implementation by avoiding the use of the Hilbert transform. The present paper can also be viewed as a prologue to one important application of the Beltrami equation: it provides a detailed description of the algorithm that has been used in [ D. Gaidashev, Nonlinearity, 20 ( 1998), pp. 713 - 741] and [ D. Gaidashev and M. Yampolsky, Experiment. Math., 16 ( 2007), pp. 215 - 226] to address an important issue in complex dynamics - conjectural universality for Siegel disks.

Place, publisher, year, edition, pages
2008. Vol. 46, no 5, 2238-2253 p.
Keyword [en]
Beltrami equation, Hilbert transform, Cauchy transform, measurable Riemann mapping, quasi-conformal map
National Category
URN: urn:nbn:se:kth:diva-33352DOI: 10.1137/050640710ISI: 000257746600002ScopusID: 2-s2.0-55349112909OAI: diva2:414668
QC 20110504Available from: 2011-05-04 Created: 2011-05-04 Last updated: 2011-05-04Bibliographically approved

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