Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations
In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonline...
Gespeichert in:
| Veröffentlicht in: | Mathematical methods in the applied sciences 2020-05, Vol.43 (8), p.5212-5233 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 5233 |
|---|---|
| container_issue | 8 |
| container_start_page | 5212 |
| container_title | Mathematical methods in the applied sciences |
| container_volume | 43 |
| creator | Saffarzadeh, Masoud Heydari, Mohammad Barid Loghmani, Ghasem |
| description | In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied. Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic
θ‐method. |
| doi_str_mv | 10.1002/mma.6261 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2391790464</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2391790464</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2931-85d045a49ff668ec975298966e3ed12e55db07df2231fcdfbb9cd15c70bf1d183</originalsourceid><addsrcrecordid>eNp10E1KAzEUB_AgCtYqeISAGzdT8zKfWZbiR6HiRt0OaSZpUzKTNkkrs_MIHsYbeBNPYmrdusoj78cf3h-hSyAjIITetC0fFbSAIzQAwlgCWVkcowGBkiQZhewUnXm_IoRUAHSA-ontdtItZCck5h03vdceWxVnrIN0POhdXJiFdTosWxws9tbEL9_7INu97GxndCe5wz5YseQ-aIGn4evz-_3j1ZoY4jjWXZALxw2Wm23MtJ0_RyeKGy8v_t4herm7fZ48JLOn--lkPEsEZSkkVd6QLOcZU6ooKilYmVNWsaKQqWyAyjxv5qRsFKUpKNGo-ZyJBnJRkrmCBqp0iK4OuWtnN1vpQ72yWxcv9TVNGZSMZEUW1fVBCWe9d1LVa6db7voaSL0vto7F1vtiI00O9E0b2f_r6sfH8a__AYHHffE</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2391790464</pqid></control><display><type>article</type><title>Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations</title><source>Wiley Online Library All Journals</source><creator>Saffarzadeh, Masoud ; Heydari, Mohammad ; Barid Loghmani, Ghasem</creator><creatorcontrib>Saffarzadeh, Masoud ; Heydari, Mohammad ; Barid Loghmani, Ghasem</creatorcontrib><description>In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied. Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic
θ‐method.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.6261</identifier><language>eng</language><publisher>Freiburg: Wiley Subscription Services, Inc</publisher><subject>Convergence ; Integral equations ; Interpolation ; Iterative algorithms ; Iterative methods ; linear spline interpolation ; Mathematical analysis ; multiple stock models ; Nonlinear equations ; pendulum problem ; predator‐prey models ; successive approximations method ; system of stochastic Volterra integral equations ; Upper bounds ; Volterra integral equations</subject><ispartof>Mathematical methods in the applied sciences, 2020-05, Vol.43 (8), p.5212-5233</ispartof><rights>2020 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2931-85d045a49ff668ec975298966e3ed12e55db07df2231fcdfbb9cd15c70bf1d183</citedby><cites>FETCH-LOGICAL-c2931-85d045a49ff668ec975298966e3ed12e55db07df2231fcdfbb9cd15c70bf1d183</cites><orcidid>0000-0002-4024-980X</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.6261$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.6261$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1416,27923,27924,45573,45574</link.rule.ids></links><search><creatorcontrib>Saffarzadeh, Masoud</creatorcontrib><creatorcontrib>Heydari, Mohammad</creatorcontrib><creatorcontrib>Barid Loghmani, Ghasem</creatorcontrib><title>Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations</title><title>Mathematical methods in the applied sciences</title><description>In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied. Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic
θ‐method.</description><subject>Convergence</subject><subject>Integral equations</subject><subject>Interpolation</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>linear spline interpolation</subject><subject>Mathematical analysis</subject><subject>multiple stock models</subject><subject>Nonlinear equations</subject><subject>pendulum problem</subject><subject>predator‐prey models</subject><subject>successive approximations method</subject><subject>system of stochastic Volterra integral equations</subject><subject>Upper bounds</subject><subject>Volterra integral equations</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp10E1KAzEUB_AgCtYqeISAGzdT8zKfWZbiR6HiRt0OaSZpUzKTNkkrs_MIHsYbeBNPYmrdusoj78cf3h-hSyAjIITetC0fFbSAIzQAwlgCWVkcowGBkiQZhewUnXm_IoRUAHSA-ontdtItZCck5h03vdceWxVnrIN0POhdXJiFdTosWxws9tbEL9_7INu97GxndCe5wz5YseQ-aIGn4evz-_3j1ZoY4jjWXZALxw2Wm23MtJ0_RyeKGy8v_t4herm7fZ48JLOn--lkPEsEZSkkVd6QLOcZU6ooKilYmVNWsaKQqWyAyjxv5qRsFKUpKNGo-ZyJBnJRkrmCBqp0iK4OuWtnN1vpQ72yWxcv9TVNGZSMZEUW1fVBCWe9d1LVa6db7voaSL0vto7F1vtiI00O9E0b2f_r6sfH8a__AYHHffE</recordid><startdate>20200530</startdate><enddate>20200530</enddate><creator>Saffarzadeh, Masoud</creator><creator>Heydari, Mohammad</creator><creator>Barid Loghmani, Ghasem</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-4024-980X</orcidid></search><sort><creationdate>20200530</creationdate><title>Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations</title><author>Saffarzadeh, Masoud ; Heydari, Mohammad ; Barid Loghmani, Ghasem</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2931-85d045a49ff668ec975298966e3ed12e55db07df2231fcdfbb9cd15c70bf1d183</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Convergence</topic><topic>Integral equations</topic><topic>Interpolation</topic><topic>Iterative algorithms</topic><topic>Iterative methods</topic><topic>linear spline interpolation</topic><topic>Mathematical analysis</topic><topic>multiple stock models</topic><topic>Nonlinear equations</topic><topic>pendulum problem</topic><topic>predator‐prey models</topic><topic>successive approximations method</topic><topic>system of stochastic Volterra integral equations</topic><topic>Upper bounds</topic><topic>Volterra integral equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Saffarzadeh, Masoud</creatorcontrib><creatorcontrib>Heydari, Mohammad</creatorcontrib><creatorcontrib>Barid Loghmani, Ghasem</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Saffarzadeh, Masoud</au><au>Heydari, Mohammad</au><au>Barid Loghmani, Ghasem</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2020-05-30</date><risdate>2020</risdate><volume>43</volume><issue>8</issue><spage>5212</spage><epage>5233</epage><pages>5212-5233</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied. Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic
θ‐method.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.6261</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0002-4024-980X</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0170-4214 |
| ispartof | Mathematical methods in the applied sciences, 2020-05, Vol.43 (8), p.5212-5233 |
| issn | 0170-4214 1099-1476 |
| language | eng |
| recordid | cdi_proquest_journals_2391790464 |
| source | Wiley Online Library All Journals |
| subjects | Convergence Integral equations Interpolation Iterative algorithms Iterative methods linear spline interpolation Mathematical analysis multiple stock models Nonlinear equations pendulum problem predator‐prey models successive approximations method system of stochastic Volterra integral equations Upper bounds Volterra integral equations |
| title | Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T16%3A38%3A42IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Convergence%20analysis%20of%20an%20iterative%20algorithm%20to%20solve%20system%20of%20nonlinear%20stochastic%20It%C3%B4%E2%80%90Volterra%20integral%20equations&rft.jtitle=Mathematical%20methods%20in%20the%20applied%20sciences&rft.au=Saffarzadeh,%20Masoud&rft.date=2020-05-30&rft.volume=43&rft.issue=8&rft.spage=5212&rft.epage=5233&rft.pages=5212-5233&rft.issn=0170-4214&rft.eissn=1099-1476&rft_id=info:doi/10.1002/mma.6261&rft_dat=%3Cproquest_cross%3E2391790464%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2391790464&rft_id=info:pmid/&rfr_iscdi=true |