Classical theory of Runge–Kutta methods for Volterra functional differential equations
For solving Volterra functional differential equations (VFDEs), a class of discrete Runge–Kutta methods based on canonical interpolation is studied, which was first presented by the same author in a previous published paper, classical stability and convergence theories for this class of methods are...
Gespeichert in:
| Veröffentlicht in: | Applied mathematics and computation 2014-03, Vol.230, p.78-95 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 95 |
|---|---|
| container_issue | |
| container_start_page | 78 |
| container_title | Applied mathematics and computation |
| container_volume | 230 |
| creator | Shoufu, Li |
| description | For solving Volterra functional differential equations (VFDEs), a class of discrete Runge–Kutta methods based on canonical interpolation is studied, which was first presented by the same author in a previous published paper, classical stability and convergence theories for this class of methods are established. The methods studied and the theories established in this paper can be directly applied to non-stiff non-linear initial value problems in delay differential equations (DDEs), integro-differential equations (IDEs), delay integro-differential equations (DIDEs), and VFDEs of other type which appear in practice, and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff VFDEs. |
| doi_str_mv | 10.1016/j.amc.2013.12.090 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1530982846</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0096300313013805</els_id><sourcerecordid>1530982846</sourcerecordid><originalsourceid>FETCH-LOGICAL-c330t-a19ec835d32d73798fd70f8fa9a1752b7088f5edc65ca82a7e0011d50122e1293</originalsourceid><addsrcrecordid>eNp9kM9KJDEQh8OisOPoA3jro5duq5Lp7jSeZPDPorAgKnsLMak4GXo6mqSFufkO-4Y-yfYwnvdU_IrfV1AfY6cIFQI25-tKb0zFAUWFvIIOfrAZylaUdbPoDtgMoGtKASB-sqOU1gDQNriYsT_LXqfkje6LvKIQt0VwxcM4vNLX59-7MWddbCivgk2FC7F4Dn2mGHXhxsFkH4aJs945ijRkPwV6H_Vun47ZodN9opPvOWdP11ePy9vy_vfNr-XlfWmEgFxq7MhIUVvBbSvaTjrbgpNOdxrbmr-0IKWryZqmNlpy3RIAoq0BOSfknZizs_3dtxjeR0pZbXwy1Pd6oDAmhbWATnK5aKYq7qsmhpQiOfUW_UbHrUJQO4tqrSaLamdRIVeTxYm52DM0_fDhKapkPA2GrI9ksrLB_4f-B9PbfAY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1530982846</pqid></control><display><type>article</type><title>Classical theory of Runge–Kutta methods for Volterra functional differential equations</title><source>Elsevier ScienceDirect Journals</source><creator>Shoufu, Li</creator><creatorcontrib>Shoufu, Li</creatorcontrib><description>For solving Volterra functional differential equations (VFDEs), a class of discrete Runge–Kutta methods based on canonical interpolation is studied, which was first presented by the same author in a previous published paper, classical stability and convergence theories for this class of methods are established. The methods studied and the theories established in this paper can be directly applied to non-stiff non-linear initial value problems in delay differential equations (DDEs), integro-differential equations (IDEs), delay integro-differential equations (DIDEs), and VFDEs of other type which appear in practice, and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff VFDEs.</description><identifier>ISSN: 0096-3003</identifier><identifier>EISSN: 1873-5649</identifier><identifier>DOI: 10.1016/j.amc.2013.12.090</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Canonical interpolation operator ; Convergence ; Delay ; Differential equations ; Initial value problems ; Interpolation ; Mathematical analysis ; Non-stiff non-linear initial value problems ; Nonlinearity ; Numerical stability ; Runge-Kutta method ; Runge–Kutta methods ; Volterra functional differential equations</subject><ispartof>Applied mathematics and computation, 2014-03, Vol.230, p.78-95</ispartof><rights>2013 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c330t-a19ec835d32d73798fd70f8fa9a1752b7088f5edc65ca82a7e0011d50122e1293</citedby><cites>FETCH-LOGICAL-c330t-a19ec835d32d73798fd70f8fa9a1752b7088f5edc65ca82a7e0011d50122e1293</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0096300313013805$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Shoufu, Li</creatorcontrib><title>Classical theory of Runge–Kutta methods for Volterra functional differential equations</title><title>Applied mathematics and computation</title><description>For solving Volterra functional differential equations (VFDEs), a class of discrete Runge–Kutta methods based on canonical interpolation is studied, which was first presented by the same author in a previous published paper, classical stability and convergence theories for this class of methods are established. The methods studied and the theories established in this paper can be directly applied to non-stiff non-linear initial value problems in delay differential equations (DDEs), integro-differential equations (IDEs), delay integro-differential equations (DIDEs), and VFDEs of other type which appear in practice, and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff VFDEs.</description><subject>Canonical interpolation operator</subject><subject>Convergence</subject><subject>Delay</subject><subject>Differential equations</subject><subject>Initial value problems</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Non-stiff non-linear initial value problems</subject><subject>Nonlinearity</subject><subject>Numerical stability</subject><subject>Runge-Kutta method</subject><subject>Runge–Kutta methods</subject><subject>Volterra functional differential equations</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kM9KJDEQh8OisOPoA3jro5duq5Lp7jSeZPDPorAgKnsLMak4GXo6mqSFufkO-4Y-yfYwnvdU_IrfV1AfY6cIFQI25-tKb0zFAUWFvIIOfrAZylaUdbPoDtgMoGtKASB-sqOU1gDQNriYsT_LXqfkje6LvKIQt0VwxcM4vNLX59-7MWddbCivgk2FC7F4Dn2mGHXhxsFkH4aJs945ijRkPwV6H_Vun47ZodN9opPvOWdP11ePy9vy_vfNr-XlfWmEgFxq7MhIUVvBbSvaTjrbgpNOdxrbmr-0IKWryZqmNlpy3RIAoq0BOSfknZizs_3dtxjeR0pZbXwy1Pd6oDAmhbWATnK5aKYq7qsmhpQiOfUW_UbHrUJQO4tqrSaLamdRIVeTxYm52DM0_fDhKapkPA2GrI9ksrLB_4f-B9PbfAY</recordid><startdate>20140301</startdate><enddate>20140301</enddate><creator>Shoufu, Li</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20140301</creationdate><title>Classical theory of Runge–Kutta methods for Volterra functional differential equations</title><author>Shoufu, Li</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c330t-a19ec835d32d73798fd70f8fa9a1752b7088f5edc65ca82a7e0011d50122e1293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Canonical interpolation operator</topic><topic>Convergence</topic><topic>Delay</topic><topic>Differential equations</topic><topic>Initial value problems</topic><topic>Interpolation</topic><topic>Mathematical analysis</topic><topic>Non-stiff non-linear initial value problems</topic><topic>Nonlinearity</topic><topic>Numerical stability</topic><topic>Runge-Kutta method</topic><topic>Runge–Kutta methods</topic><topic>Volterra functional differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shoufu, Li</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</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><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shoufu, Li</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Classical theory of Runge–Kutta methods for Volterra functional differential equations</atitle><jtitle>Applied mathematics and computation</jtitle><date>2014-03-01</date><risdate>2014</risdate><volume>230</volume><spage>78</spage><epage>95</epage><pages>78-95</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><abstract>For solving Volterra functional differential equations (VFDEs), a class of discrete Runge–Kutta methods based on canonical interpolation is studied, which was first presented by the same author in a previous published paper, classical stability and convergence theories for this class of methods are established. The methods studied and the theories established in this paper can be directly applied to non-stiff non-linear initial value problems in delay differential equations (DDEs), integro-differential equations (IDEs), delay integro-differential equations (DIDEs), and VFDEs of other type which appear in practice, and can be used as a necessary basis for the study of splitting methods for complex nonlinear stiff VFDEs.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.amc.2013.12.090</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0096-3003 |
| ispartof | Applied mathematics and computation, 2014-03, Vol.230, p.78-95 |
| issn | 0096-3003 1873-5649 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1530982846 |
| source | Elsevier ScienceDirect Journals |
| subjects | Canonical interpolation operator Convergence Delay Differential equations Initial value problems Interpolation Mathematical analysis Non-stiff non-linear initial value problems Nonlinearity Numerical stability Runge-Kutta method Runge–Kutta methods Volterra functional differential equations |
| title | Classical theory of Runge–Kutta methods for Volterra functional differential equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T08%3A42%3A32IST&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=Classical%20theory%20of%20Runge%E2%80%93Kutta%20methods%20for%20Volterra%20functional%20differential%20equations&rft.jtitle=Applied%20mathematics%20and%20computation&rft.au=Shoufu,%20Li&rft.date=2014-03-01&rft.volume=230&rft.spage=78&rft.epage=95&rft.pages=78-95&rft.issn=0096-3003&rft.eissn=1873-5649&rft_id=info:doi/10.1016/j.amc.2013.12.090&rft_dat=%3Cproquest_cross%3E1530982846%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=1530982846&rft_id=info:pmid/&rft_els_id=S0096300313013805&rfr_iscdi=true |