Loading…

Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation

A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several e...

Full description

Saved in:

Bibliographic Details
Published in:	Acoustics (Basel, Switzerland) Switzerland), 2021-03, Vol.3 (1), p.212-220
Main Author:	Vanhille, Christian
Format:	Article
Language:	English
Subjects:	Acoustics Algorithms Approximation Integrals Iterative algorithms Iterative methods linear iterative procedure Linear systems Model accuracy nonlinear acoustics nonlinear Rayleigh–Plesset equation Nonlinear systems Ordinary differential equations Problem solving
Citations:	Items that this one cites Items that cite this one
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

cited_by	cdi_FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413
cites	cdi_FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413
container_end_page	220
container_issue	1
container_start_page	212
container_title	Acoustics (Basel, Switzerland)
container_volume	3
creator	Vanhille, Christian
description	A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several examples of different physical meanings. The simplicity and usefulness of the presented method here in relation to the direct resolution of the whole nonlinear system, which is also discussed, make the method very attractive to solving a problem. This iterative method allows us to solve only linear systems instead of the nonlinear differential problem. Moreover, the implementation of the iterative algorithm includes a tolerance-dependent stopping criterion that is also tested.
doi_str_mv	10.3390/acoustics3010015
format	article
fullrecord	<record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_f2b3912a96514c8e9f55c332eeab94c7</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_f2b3912a96514c8e9f55c332eeab94c7</doaj_id><sourcerecordid>2519512034</sourcerecordid><originalsourceid>FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413</originalsourceid><addsrcrecordid>eNpdkE1LA0EMhgdRsNTePS54Xp3P7c6xlKqFgsUP8DZkZ7N1y9ppZ2YFb_4H_6G_xNGKiIeQ8CZ5El5CThk9F0LTC7CuD7G1QVBGKVMHZMALLnOl9ePhn_qYjEJYU0o5l6woiwGZLNoNgs_mET3E9gWzpXcW695jFl1257okQXYLrx22q6ePt_dlhyFgzGa7Pi24zQk5aqALOPrJQ_JwObufXueLm6v5dLLIraA65twiSIU1WIsF0qbmGnQBDUNR1qixaGoNAmHMADUrU6_C0hZoU1RUMjEk8z23drA2W98-g381DlrzLTi_MuCTBx2ahldCM54Yiklbom6UskJwRKi0tOPEOtuztt7tegzRrF3vN-l9wxXTinEqZJqi-ynrXQgem9-rjJov381_38UnJX96Mg</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2519512034</pqid></control><display><type>article</type><title>Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation</title><source>Publicly Available Content Database</source><source>EZB Electronic Journals Library</source><creator>Vanhille, Christian</creator><creatorcontrib>Vanhille, Christian</creatorcontrib><description>A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several examples of different physical meanings. The simplicity and usefulness of the presented method here in relation to the direct resolution of the whole nonlinear system, which is also discussed, make the method very attractive to solving a problem. This iterative method allows us to solve only linear systems instead of the nonlinear differential problem. Moreover, the implementation of the iterative algorithm includes a tolerance-dependent stopping criterion that is also tested.</description><identifier>ISSN: 2624-599X</identifier><identifier>EISSN: 2624-599X</identifier><identifier>DOI: 10.3390/acoustics3010015</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Acoustics ; Algorithms ; Approximation ; Integrals ; Iterative algorithms ; Iterative methods ; linear iterative procedure ; Linear systems ; Model accuracy ; nonlinear acoustics ; nonlinear Rayleigh–Plesset equation ; Nonlinear systems ; Ordinary differential equations ; Problem solving</subject><ispartof>Acoustics (Basel, Switzerland), 2021-03, Vol.3 (1), p.212-220</ispartof><rights>2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413</citedby><cites>FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413</cites><orcidid>0000-0002-1578-2602</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2519512034/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2519512034?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,25731,27901,27902,36989,44566,74869</link.rule.ids></links><search><creatorcontrib>Vanhille, Christian</creatorcontrib><title>Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation</title><title>Acoustics (Basel, Switzerland)</title><description>A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several examples of different physical meanings. The simplicity and usefulness of the presented method here in relation to the direct resolution of the whole nonlinear system, which is also discussed, make the method very attractive to solving a problem. This iterative method allows us to solve only linear systems instead of the nonlinear differential problem. Moreover, the implementation of the iterative algorithm includes a tolerance-dependent stopping criterion that is also tested.</description><subject>Acoustics</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Integrals</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>linear iterative procedure</subject><subject>Linear systems</subject><subject>Model accuracy</subject><subject>nonlinear acoustics</subject><subject>nonlinear Rayleigh–Plesset equation</subject><subject>Nonlinear systems</subject><subject>Ordinary differential equations</subject><subject>Problem solving</subject><issn>2624-599X</issn><issn>2624-599X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNpdkE1LA0EMhgdRsNTePS54Xp3P7c6xlKqFgsUP8DZkZ7N1y9ppZ2YFb_4H_6G_xNGKiIeQ8CZ5El5CThk9F0LTC7CuD7G1QVBGKVMHZMALLnOl9ePhn_qYjEJYU0o5l6woiwGZLNoNgs_mET3E9gWzpXcW695jFl1257okQXYLrx22q6ePt_dlhyFgzGa7Pi24zQk5aqALOPrJQ_JwObufXueLm6v5dLLIraA65twiSIU1WIsF0qbmGnQBDUNR1qixaGoNAmHMADUrU6_C0hZoU1RUMjEk8z23drA2W98-g381DlrzLTi_MuCTBx2ahldCM54Yiklbom6UskJwRKi0tOPEOtuztt7tegzRrF3vN-l9wxXTinEqZJqi-ynrXQgem9-rjJov381_38UnJX96Mg</recordid><startdate>20210301</startdate><enddate>20210301</enddate><creator>Vanhille, Christian</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0002-1578-2602</orcidid></search><sort><creationdate>20210301</creationdate><title>Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation</title><author>Vanhille, Christian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Acoustics</topic><topic>Algorithms</topic><topic>Approximation</topic><topic>Integrals</topic><topic>Iterative algorithms</topic><topic>Iterative methods</topic><topic>linear iterative procedure</topic><topic>Linear systems</topic><topic>Model accuracy</topic><topic>nonlinear acoustics</topic><topic>nonlinear Rayleigh–Plesset equation</topic><topic>Nonlinear systems</topic><topic>Ordinary differential equations</topic><topic>Problem solving</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vanhille, Christian</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Acoustics (Basel, Switzerland)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vanhille, Christian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation</atitle><jtitle>Acoustics (Basel, Switzerland)</jtitle><date>2021-03-01</date><risdate>2021</risdate><volume>3</volume><issue>1</issue><spage>212</spage><epage>220</epage><pages>212-220</pages><issn>2624-599X</issn><eissn>2624-599X</eissn><abstract>A nonlinear Rayleigh–Plesset equation for describing the behavior of a gas bubble in an acoustic field written in terms of bubble-volume variation is solved through a linear iterative procedure. The model is validated, and its accuracy and fast convergence are shown through the analysis of several examples of different physical meanings. The simplicity and usefulness of the presented method here in relation to the direct resolution of the whole nonlinear system, which is also discussed, make the method very attractive to solving a problem. This iterative method allows us to solve only linear systems instead of the nonlinear differential problem. Moreover, the implementation of the iterative algorithm includes a tolerance-dependent stopping criterion that is also tested.</abstract><cop>Basel</cop><pub>MDPI AG</pub><doi>10.3390/acoustics3010015</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0002-1578-2602</orcidid><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 2624-599X
ispartof	Acoustics (Basel, Switzerland), 2021-03, Vol.3 (1), p.212-220
issn	2624-599X 2624-599X
language	eng
recordid	cdi_doaj_primary_oai_doaj_org_article_f2b3912a96514c8e9f55c332eeab94c7
source	Publicly Available Content Database; EZB Electronic Journals Library
subjects	Acoustics Algorithms Approximation Integrals Iterative algorithms Iterative methods linear iterative procedure Linear systems Model accuracy nonlinear acoustics nonlinear Rayleigh–Plesset equation Nonlinear systems Ordinary differential equations Problem solving
title	Linear Iterative Procedure to Solve a Rayleigh–Plesset Equation
url	http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T01%3A41%3A14IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Linear%20Iterative%20Procedure%20to%20Solve%20a%20Rayleigh%E2%80%93Plesset%20Equation&rft.jtitle=Acoustics%20(Basel,%20Switzerland)&rft.au=Vanhille,%20Christian&rft.date=2021-03-01&rft.volume=3&rft.issue=1&rft.spage=212&rft.epage=220&rft.pages=212-220&rft.issn=2624-599X&rft.eissn=2624-599X&rft_id=info:doi/10.3390/acoustics3010015&rft_dat=%3Cproquest_doaj_%3E2519512034%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c309t-2cea45edacce6e0fd29a96af1e38de9e6fd9a3ea71ae918a96be8c6ecc6eb0413%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2519512034&rft_id=info:pmid/&rfr_iscdi=true