Numerical Solution of a Nonlinear Integro-Differential Equation

A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral...

Full description

Saved in:
Bibliographic Details
Main Authors: Buša, Ján, Hnatič, Michal, Honkonen, Juha, Lučivjanský, Tomáš
Format: Conference Proceeding
Language:English
Subjects:
Algorithms
Approximation
Density
Differential equations
Integrals
Mathematical analysis
Mathematical models
Operators (mathematics)
Regularization
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-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3
cites cdi_FETCH-LOGICAL-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3
container_end_page
container_issue
container_start_page 2017
container_title
container_volume 108
creator Buša, Ján
Hnatič, Michal
Honkonen, Juha
Lučivjanský, Tomáš
description A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral entering the equation is divergent) uses regularization and then finite differences for the approximation of the differential operator together with a piecewise linear approximation of a(t) under the integral. The presented numerical results point to basic features of the behavior of the number density function a(t) and suggest further improvement of the proposed algorithm.
doi_str_mv 10.1051/epjconf/201610802017
format conference_proceeding
fullrecord <record><control><sourceid>proquest_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_b0abb784bb8f4dc29cf6441f2710ee13</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_b0abb784bb8f4dc29cf6441f2710ee13</doaj_id><sourcerecordid>4042807661</sourcerecordid><originalsourceid>FETCH-LOGICAL-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3</originalsourceid><addsrcrecordid>eNpNkE1LAzEQhoMoWGr_gYcFz2uTSfYjJ5FatVDqQQVvIclOSpbtps3uHvz3bm0R5zLD8PDM8BJyy-g9oxmb4762oXVzoCxntKRjLy7IBBilKWXi6_LffE1mXVfTsbiUPMsn5GEz7DB6q5vkPTRD70ObBJfoZBPaxreoY7Jqe9zGkD555zBi2_sRXh4GfYRvyJXTTYezc5-Sz-flx-I1Xb-9rBaP69RyyfoUwHAjhWFYCSOhRClAV9bozAlRaidsacBSmsvKZkClBp6BASkEA3CIfEpWJ28VdK320e90_FZBe_W7CHGrdOy9bVAZqo0pSmFM6URlQVqXjx4HBaOIjI-uu5NrH8NhwK5XdRhiO76vWFHmkHPI8pESJ8rG0HUR3d9VRtUxeXVOXv1Pnv8A5QV3lA</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>conference_proceeding</recordtype><pqid>1786263256</pqid></control><display><type>conference_proceeding</type><title>Numerical Solution of a Nonlinear Integro-Differential Equation</title><source>Access via ProQuest (Open Access)</source><source>Free Full-Text Journals in Chemistry</source><creator>Buša, Ján ; Hnatič, Michal ; Honkonen, Juha ; Lučivjanský, Tomáš</creator><contributor>Adam, Gh ; Buša, J. ; Hnatič, M.</contributor><creatorcontrib>Buša, Ján ; Hnatič, Michal ; Honkonen, Juha ; Lučivjanský, Tomáš ; Adam, Gh ; Buša, J. ; Hnatič, M.</creatorcontrib><description>A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral entering the equation is divergent) uses regularization and then finite differences for the approximation of the differential operator together with a piecewise linear approximation of a(t) under the integral. The presented numerical results point to basic features of the behavior of the number density function a(t) and suggest further improvement of the proposed algorithm.</description><identifier>ISSN: 2100-014X</identifier><identifier>ISSN: 2101-6275</identifier><identifier>EISSN: 2100-014X</identifier><identifier>DOI: 10.1051/epjconf/201610802017</identifier><language>eng</language><publisher>Les Ulis: EDP Sciences</publisher><subject>Algorithms ; Approximation ; Density ; Differential equations ; Integrals ; Mathematical analysis ; Mathematical models ; Operators (mathematics) ; Regularization</subject><ispartof>EPJ Web of Conferences, 2016, Vol.108, p.2017</ispartof><rights>2016. This work is licensed under http://creativecommons.org/licenses/by/4.0/ (the “License”). 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-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3</citedby><cites>FETCH-LOGICAL-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/1786263256?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,25753,27924,27925,37012,44590</link.rule.ids></links><search><contributor>Adam, Gh</contributor><contributor>Buša, J.</contributor><contributor>Hnatič, M.</contributor><creatorcontrib>Buša, Ján</creatorcontrib><creatorcontrib>Hnatič, Michal</creatorcontrib><creatorcontrib>Honkonen, Juha</creatorcontrib><creatorcontrib>Lučivjanský, Tomáš</creatorcontrib><title>Numerical Solution of a Nonlinear Integro-Differential Equation</title><title>EPJ Web of Conferences</title><description>A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral entering the equation is divergent) uses regularization and then finite differences for the approximation of the differential operator together with a piecewise linear approximation of a(t) under the integral. The presented numerical results point to basic features of the behavior of the number density function a(t) and suggest further improvement of the proposed algorithm.</description><subject>Algorithms</subject><subject>Approximation</subject><subject>Density</subject><subject>Differential equations</subject><subject>Integrals</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Operators (mathematics)</subject><subject>Regularization</subject><issn>2100-014X</issn><issn>2101-6275</issn><issn>2100-014X</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2016</creationdate><recordtype>conference_proceeding</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNpNkE1LAzEQhoMoWGr_gYcFz2uTSfYjJ5FatVDqQQVvIclOSpbtps3uHvz3bm0R5zLD8PDM8BJyy-g9oxmb4762oXVzoCxntKRjLy7IBBilKWXi6_LffE1mXVfTsbiUPMsn5GEz7DB6q5vkPTRD70ObBJfoZBPaxreoY7Jqe9zGkD555zBi2_sRXh4GfYRvyJXTTYezc5-Sz-flx-I1Xb-9rBaP69RyyfoUwHAjhWFYCSOhRClAV9bozAlRaidsacBSmsvKZkClBp6BASkEA3CIfEpWJ28VdK320e90_FZBe_W7CHGrdOy9bVAZqo0pSmFM6URlQVqXjx4HBaOIjI-uu5NrH8NhwK5XdRhiO76vWFHmkHPI8pESJ8rG0HUR3d9VRtUxeXVOXv1Pnv8A5QV3lA</recordid><startdate>20160101</startdate><enddate>20160101</enddate><creator>Buša, Ján</creator><creator>Hnatič, Michal</creator><creator>Honkonen, Juha</creator><creator>Lučivjanský, Tomáš</creator><general>EDP Sciences</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></search><sort><creationdate>20160101</creationdate><title>Numerical Solution of a Nonlinear Integro-Differential Equation</title><author>Buša, Ján ; Hnatič, Michal ; Honkonen, Juha ; Lučivjanský, Tomáš</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algorithms</topic><topic>Approximation</topic><topic>Density</topic><topic>Differential equations</topic><topic>Integrals</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Operators (mathematics)</topic><topic>Regularization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Buša, Ján</creatorcontrib><creatorcontrib>Hnatič, Michal</creatorcontrib><creatorcontrib>Honkonen, Juha</creatorcontrib><creatorcontrib>Lučivjanský, Tomáš</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 &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest advanced technologies &amp; aerospace journals</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Access via ProQuest (Open Access)</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></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Buša, Ján</au><au>Hnatič, Michal</au><au>Honkonen, Juha</au><au>Lučivjanský, Tomáš</au><au>Adam, Gh</au><au>Buša, J.</au><au>Hnatič, M.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Numerical Solution of a Nonlinear Integro-Differential Equation</atitle><btitle>EPJ Web of Conferences</btitle><date>2016-01-01</date><risdate>2016</risdate><volume>108</volume><spage>2017</spage><pages>2017-</pages><issn>2100-014X</issn><issn>2101-6275</issn><eissn>2100-014X</eissn><abstract>A discretization algorithm for the numerical solution of a nonlinear integrodifferential equation modeling the temporal variation of the mean number density a(t) in the single-species annihilation reaction A + A → 0 is discussed. The proposed solution for the two-dimensional case (where the integral entering the equation is divergent) uses regularization and then finite differences for the approximation of the differential operator together with a piecewise linear approximation of a(t) under the integral. The presented numerical results point to basic features of the behavior of the number density function a(t) and suggest further improvement of the proposed algorithm.</abstract><cop>Les Ulis</cop><pub>EDP Sciences</pub><doi>10.1051/epjconf/201610802017</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 2100-014X
ispartof EPJ Web of Conferences, 2016, Vol.108, p.2017
issn 2100-014X
2101-6275
2100-014X
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_b0abb784bb8f4dc29cf6441f2710ee13
source Access via ProQuest (Open Access); Free Full-Text Journals in Chemistry
subjects Algorithms
Approximation
Density
Differential equations
Integrals
Mathematical analysis
Mathematical models
Operators (mathematics)
Regularization
title Numerical Solution of a Nonlinear Integro-Differential Equation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T11%3A31%3A08IST&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:book&rft.genre=proceeding&rft.atitle=Numerical%20Solution%20of%20a%20Nonlinear%20Integro-Differential%20Equation&rft.btitle=EPJ%20Web%20of%20Conferences&rft.au=Bu%C5%A1a,%20J%C3%A1n&rft.date=2016-01-01&rft.volume=108&rft.spage=2017&rft.pages=2017-&rft.issn=2100-014X&rft.eissn=2100-014X&rft_id=info:doi/10.1051/epjconf/201610802017&rft_dat=%3Cproquest_doaj_%3E4042807661%3C/proquest_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c391t-22b3b94b1ed4b928e942adcba5f448af4c8b2c0069dc5209a2352b2944122fee3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1786263256&rft_id=info:pmid/&rfr_iscdi=true