On a numerical algorithm for the solution of the radial Loewner equation

On a numerical algorithm for the solution of the radial Loewner equation

The Loewner partial differential equation provides a one‐parametric family of conformal maps on the unit disk. The images describe a flow of an expanding simply‐connected domain, called the Loewner flow, on the complex plane. In this paper, we present a numerical algorithm for solving the radial Loe...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematical methods in the applied sciences 2018-01, Vol.41 (2), p.714-723
Hauptverfasser: Hotta, Ikkei, Shimauchi, Hirokazu
Format: Artikel
Sprache:eng
Schlagworte:
conformal mapping
Loewner differential equation
polynomial approximation
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 723
container_issue 2
container_start_page 714
container_title Mathematical methods in the applied sciences
container_volume 41
creator Hotta, Ikkei
Shimauchi, Hirokazu
description The Loewner partial differential equation provides a one‐parametric family of conformal maps on the unit disk. The images describe a flow of an expanding simply‐connected domain, called the Loewner flow, on the complex plane. In this paper, we present a numerical algorithm for solving the radial Loewner partial differential equation. The algorithm is applied to visualization of Loewner flows with the performance and precision. From the theoretical point of view, our algorithm is based on a recursive formula for determining coefficients of polynomial approximations. We prove that each coefficient converges to true values with reasonable regularity.
doi_str_mv 10.1002/mma.4640
format Article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1002_mma_4640</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>MMA4640</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2920-f4806adf9ee8ef2f5f8f330d8ae5ee0ee5bc6005712cfad964622c33a99f51553</originalsourceid><addsrcrecordid>eNp10LFOwzAQgGELgUQoSDyCRxaXs2Mn8VhVQJFSdYE5Ms6ZBiUx2Imqvj1Jy8p0Ot2nG35C7jksOYB47DqzlJmEC5Jw0JpxmWeXJAGeA5OCy2tyE-MXABSci4Rsdj01tB87DI01LTXtpw_NsO-o84EOe6TRt-PQ-J56d9qDqZsJlh4PPQaKP6OZz7fkypk24t3fXJD356e39YaVu5fX9apkVmgBzMkCMlM7jVigE065wqUp1IVBhQiI6sNmACrnwjpT60xmQtg0NVo7xZVKF-Th_NcGH2NAV32HpjPhWHGo5gLVVKCaC0yUnemhafH4r6u229XJ_wIZJF0Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On a numerical algorithm for the solution of the radial Loewner equation</title><source>Access via Wiley Online Library</source><creator>Hotta, Ikkei ; Shimauchi, Hirokazu</creator><creatorcontrib>Hotta, Ikkei ; Shimauchi, Hirokazu</creatorcontrib><description>The Loewner partial differential equation provides a one‐parametric family of conformal maps on the unit disk. The images describe a flow of an expanding simply‐connected domain, called the Loewner flow, on the complex plane. In this paper, we present a numerical algorithm for solving the radial Loewner partial differential equation. The algorithm is applied to visualization of Loewner flows with the performance and precision. From the theoretical point of view, our algorithm is based on a recursive formula for determining coefficients of polynomial approximations. We prove that each coefficient converges to true values with reasonable regularity.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.4640</identifier><language>eng</language><subject>conformal mapping ; Loewner differential equation ; polynomial approximation</subject><ispartof>Mathematical methods in the applied sciences, 2018-01, Vol.41 (2), p.714-723</ispartof><rights>Copyright © 2017 John Wiley &amp; Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2920-f4806adf9ee8ef2f5f8f330d8ae5ee0ee5bc6005712cfad964622c33a99f51553</cites><orcidid>0000-0002-9160-5667</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.4640$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.4640$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Hotta, Ikkei</creatorcontrib><creatorcontrib>Shimauchi, Hirokazu</creatorcontrib><title>On a numerical algorithm for the solution of the radial Loewner equation</title><title>Mathematical methods in the applied sciences</title><description>The Loewner partial differential equation provides a one‐parametric family of conformal maps on the unit disk. The images describe a flow of an expanding simply‐connected domain, called the Loewner flow, on the complex plane. In this paper, we present a numerical algorithm for solving the radial Loewner partial differential equation. The algorithm is applied to visualization of Loewner flows with the performance and precision. From the theoretical point of view, our algorithm is based on a recursive formula for determining coefficients of polynomial approximations. We prove that each coefficient converges to true values with reasonable regularity.</description><subject>conformal mapping</subject><subject>Loewner differential equation</subject><subject>polynomial approximation</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp10LFOwzAQgGELgUQoSDyCRxaXs2Mn8VhVQJFSdYE5Ms6ZBiUx2Imqvj1Jy8p0Ot2nG35C7jksOYB47DqzlJmEC5Jw0JpxmWeXJAGeA5OCy2tyE-MXABSci4Rsdj01tB87DI01LTXtpw_NsO-o84EOe6TRt-PQ-J56d9qDqZsJlh4PPQaKP6OZz7fkypk24t3fXJD356e39YaVu5fX9apkVmgBzMkCMlM7jVigE065wqUp1IVBhQiI6sNmACrnwjpT60xmQtg0NVo7xZVKF-Th_NcGH2NAV32HpjPhWHGo5gLVVKCaC0yUnemhafH4r6u229XJ_wIZJF0Q</recordid><startdate>20180130</startdate><enddate>20180130</enddate><creator>Hotta, Ikkei</creator><creator>Shimauchi, Hirokazu</creator><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9160-5667</orcidid></search><sort><creationdate>20180130</creationdate><title>On a numerical algorithm for the solution of the radial Loewner equation</title><author>Hotta, Ikkei ; Shimauchi, Hirokazu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2920-f4806adf9ee8ef2f5f8f330d8ae5ee0ee5bc6005712cfad964622c33a99f51553</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>conformal mapping</topic><topic>Loewner differential equation</topic><topic>polynomial approximation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hotta, Ikkei</creatorcontrib><creatorcontrib>Shimauchi, Hirokazu</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hotta, Ikkei</au><au>Shimauchi, Hirokazu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a numerical algorithm for the solution of the radial Loewner equation</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2018-01-30</date><risdate>2018</risdate><volume>41</volume><issue>2</issue><spage>714</spage><epage>723</epage><pages>714-723</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>The Loewner partial differential equation provides a one‐parametric family of conformal maps on the unit disk. The images describe a flow of an expanding simply‐connected domain, called the Loewner flow, on the complex plane. In this paper, we present a numerical algorithm for solving the radial Loewner partial differential equation. The algorithm is applied to visualization of Loewner flows with the performance and precision. From the theoretical point of view, our algorithm is based on a recursive formula for determining coefficients of polynomial approximations. We prove that each coefficient converges to true values with reasonable regularity.</abstract><doi>10.1002/mma.4640</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-9160-5667</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0170-4214
ispartof Mathematical methods in the applied sciences, 2018-01, Vol.41 (2), p.714-723
issn 0170-4214
1099-1476
language eng
recordid cdi_crossref_primary_10_1002_mma_4640
source Access via Wiley Online Library
subjects conformal mapping
Loewner differential equation
polynomial approximation
title On a numerical algorithm for the solution of the radial Loewner equation
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T21%3A58%3A46IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20a%20numerical%20algorithm%20for%20the%20solution%20of%20the%20radial%20Loewner%20equation&rft.jtitle=Mathematical%20methods%20in%20the%20applied%20sciences&rft.au=Hotta,%20Ikkei&rft.date=2018-01-30&rft.volume=41&rft.issue=2&rft.spage=714&rft.epage=723&rft.pages=714-723&rft.issn=0170-4214&rft.eissn=1099-1476&rft_id=info:doi/10.1002/mma.4640&rft_dat=%3Cwiley_cross%3EMMA4640%3C/wiley_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true