Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type
This paper is concerned with the numerical properties of θ -methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two θ -methods, namely the one-leg θ -method and the linear θ -method, the necessary and sufficient conditions u...
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| Veröffentlicht in: | Journal of computational and applied mathematics 2011, Vol.235 (5), p.1542-1552 |
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| container_title | Journal of computational and applied mathematics |
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| creator | Wang, Qi Zhu, Qingyong Liu, Mingzhu |
| description | This paper is concerned with the numerical properties of
θ
-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two
θ
-methods, namely the one-leg
θ
-method and the linear
θ
-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the
θ
-methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the
θ
-methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results. |
| doi_str_mv | 10.1016/j.cam.2010.08.041 |
| format | Article |
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θ
-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two
θ
-methods, namely the one-leg
θ
-method and the linear
θ
-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the
θ
-methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the
θ
-methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2010.08.041</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>[formula omitted]-methods ; Asymptotic stability ; Computation ; Differential equations ; Exact sciences and technology ; Exact solutions ; Mathematical analysis ; Mathematical models ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical methods in probability and statistics ; Numerical solution ; Numerical stability ; Ordinary differential equations ; Oscillation ; Oscillations ; Piecewise continuous ; Sciences and techniques of general use ; Stability</subject><ispartof>Journal of computational and applied mathematics, 2011, Vol.235 (5), p.1542-1552</ispartof><rights>2010 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c402t-9f0758ee5a85672b4bdb95b2c1167a488e653ffe95fd419fe467a44a2d3ac7b23</citedby><cites>FETCH-LOGICAL-c402t-9f0758ee5a85672b4bdb95b2c1167a488e653ffe95fd419fe467a44a2d3ac7b23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0377042710004905$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,4010,27900,27901,27902,65534</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23825538$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Wang, Qi</creatorcontrib><creatorcontrib>Zhu, Qingyong</creatorcontrib><creatorcontrib>Liu, Mingzhu</creatorcontrib><title>Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type</title><title>Journal of computational and applied mathematics</title><description>This paper is concerned with the numerical properties of
θ
-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two
θ
-methods, namely the one-leg
θ
-method and the linear
θ
-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the
θ
-methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the
θ
-methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results.</description><subject>[formula omitted]-methods</subject><subject>Asymptotic stability</subject><subject>Computation</subject><subject>Differential equations</subject><subject>Exact sciences and technology</subject><subject>Exact solutions</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical methods in probability and statistics</subject><subject>Numerical solution</subject><subject>Numerical stability</subject><subject>Ordinary differential equations</subject><subject>Oscillation</subject><subject>Oscillations</subject><subject>Piecewise continuous</subject><subject>Sciences and techniques of general use</subject><subject>Stability</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9UU2PFCEQJUYTx9Uf4I2L8dQj0HRDx5PZ-JVssgf1TGgolEkPzAK9m_kr_lprdiYe90SqePVe1XuEvOVsyxkfP-y2zu63gmHN9JZJ_oxsuFZTx5XSz8mG9Up1TAr1kryqdccYGycuN-Tvj2bnuMR2pDZ5mquLy2JbzKnSHGha91CiswuteVnP7ZAL9TEEKJBaxC-4Wy8TD7H9oYcIDh5iBeoyAtKa10pt-Y1UqT2y2qVBSbbBgqr-3iYH_lG-QLPFY9GOB3hNXgS7VHhzea_Iry-ff15_625uv36__nTTOclE66bA1KABBquHUYlZzn6ehlk4zkdlpdYwDj1uOw3BSz4FkKe2tML31qlZ9Ffk_Zn3UPLdCrWZfawO0IYEuLrRPed6QpcRyc9IV3KtBYI5lLi35Wg4M6cYzM5gDOYUg2HaYAw48-7Cbiv6GApeG-v_QdFrMQy9RtzHMw7w1PsIxWAUcHImFnDN-ByfUPkHDFOiNw</recordid><startdate>2011</startdate><enddate>2011</enddate><creator>Wang, Qi</creator><creator>Zhu, Qingyong</creator><creator>Liu, Mingzhu</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><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>2011</creationdate><title>Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type</title><author>Wang, Qi ; Zhu, Qingyong ; Liu, Mingzhu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c402t-9f0758ee5a85672b4bdb95b2c1167a488e653ffe95fd419fe467a44a2d3ac7b23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>[formula omitted]-methods</topic><topic>Asymptotic stability</topic><topic>Computation</topic><topic>Differential equations</topic><topic>Exact sciences and technology</topic><topic>Exact solutions</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical methods in probability and statistics</topic><topic>Numerical solution</topic><topic>Numerical stability</topic><topic>Ordinary differential equations</topic><topic>Oscillation</topic><topic>Oscillations</topic><topic>Piecewise continuous</topic><topic>Sciences and techniques of general use</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Qi</creatorcontrib><creatorcontrib>Zhu, Qingyong</creatorcontrib><creatorcontrib>Liu, Mingzhu</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><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>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Qi</au><au>Zhu, Qingyong</au><au>Liu, Mingzhu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2011</date><risdate>2011</risdate><volume>235</volume><issue>5</issue><spage>1542</spage><epage>1552</epage><pages>1542-1552</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>This paper is concerned with the numerical properties of
θ
-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two
θ
-methods, namely the one-leg
θ
-method and the linear
θ
-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the
θ
-methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the
θ
-methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2010.08.041</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of computational and applied mathematics, 2011, Vol.235 (5), p.1542-1552 |
| issn | 0377-0427 1879-1778 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | [formula omitted]-methods Asymptotic stability Computation Differential equations Exact sciences and technology Exact solutions Mathematical analysis Mathematical models Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Numerical solution Numerical stability Ordinary differential equations Oscillation Oscillations Piecewise continuous Sciences and techniques of general use Stability |
| title | Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type |
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