Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation
. In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated s...
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| Veröffentlicht in: | European physical journal plus 2016-10, Vol.131 (10), p.356, Article 356 |
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| creator | Ak, Turgut Battal Gazi Karakoc, S. Triki, Houria |
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In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and
a priori
error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable. |
| doi_str_mv | 10.1140/epjp/i2016-16356-3 |
| format | Article |
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In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and
a priori
error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2016-16356-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Atomic ; B spline functions ; Basis functions ; Complex Systems ; Condensed Matter Physics ; Initial conditions ; Korteweg-Devries equation ; Mathematical and Computational Physics ; Molecular ; Optical and Plasma Physics ; Physics ; Physics and Astronomy ; Regular Article ; Shallow water ; Solitary waves ; Theoretical ; Water waves</subject><ispartof>European physical journal plus, 2016-10, Vol.131 (10), p.356, Article 356</ispartof><rights>Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016</rights><rights>Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2016.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-84cb61329064d150b734e2f5bfc112449b0ca313a4e36b145c2d90a6cc39a19d3</citedby><cites>FETCH-LOGICAL-c319t-84cb61329064d150b734e2f5bfc112449b0ca313a4e36b145c2d90a6cc39a19d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/i2016-16356-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919612016?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Ak, Turgut</creatorcontrib><creatorcontrib>Battal Gazi Karakoc, S.</creatorcontrib><creatorcontrib>Triki, Houria</creatorcontrib><title>Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and
a priori
error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable.</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>B spline functions</subject><subject>Basis functions</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Initial conditions</subject><subject>Korteweg-Devries equation</subject><subject>Mathematical and Computational Physics</subject><subject>Molecular</subject><subject>Optical and Plasma Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Regular Article</subject><subject>Shallow water</subject><subject>Solitary waves</subject><subject>Theoretical</subject><subject>Water waves</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kE1LAzEQhoMoWGr_gKeA59XMJhvNUYpfWBREPRqy2Vmbst1sk2yL_95tK-jJOczM4f2Ah5BTYOcAgl1gt-guXM5AZiB5ITN-QEY5KJYVQojDP_8xmcS4YMMIBUKJEfl46pcYnDUNjW7ZNyY539LaB5oCmrTENlFf08rFDkN0a6RxbprGb-jGJAzDXmOkG5fm9MVHbE2fPVbvFFf9LumEHNWmiTj5uWPydnvzOr3PZs93D9PrWWY5qJRdCVtK4LliUlRQsPKSC8zroqwtQC6EKpk1HLgRyGUJorB5pZiR1nJlQFV8TM72uV3wqx5j0gvfh3ao1LkCJWFLZ1Dle5UNPsaAte6CW5rwpYHpLUq9Ral3KPUOpeaDie9NcRC3nxh-o_9xfQOt4Xl9</recordid><startdate>20161001</startdate><enddate>20161001</enddate><creator>Ak, Turgut</creator><creator>Battal Gazi Karakoc, S.</creator><creator>Triki, Houria</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope></search><sort><creationdate>20161001</creationdate><title>Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation</title><author>Ak, Turgut ; Battal Gazi Karakoc, S. ; Triki, Houria</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-84cb61329064d150b734e2f5bfc112449b0ca313a4e36b145c2d90a6cc39a19d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>B spline functions</topic><topic>Basis functions</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Initial conditions</topic><topic>Korteweg-Devries equation</topic><topic>Mathematical and Computational Physics</topic><topic>Molecular</topic><topic>Optical and Plasma Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Regular Article</topic><topic>Shallow water</topic><topic>Solitary waves</topic><topic>Theoretical</topic><topic>Water waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ak, Turgut</creatorcontrib><creatorcontrib>Battal Gazi Karakoc, S.</creatorcontrib><creatorcontrib>Triki, Houria</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><jtitle>European physical journal plus</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ak, Turgut</au><au>Battal Gazi Karakoc, S.</au><au>Triki, Houria</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation</atitle><jtitle>European physical journal plus</jtitle><stitle>Eur. Phys. J. Plus</stitle><date>2016-10-01</date><risdate>2016</risdate><volume>131</volume><issue>10</issue><spage>356</spage><pages>356-</pages><artnum>356</artnum><issn>2190-5444</issn><eissn>2190-5444</eissn><abstract>.
In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and
a priori
error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2016-16356-3</doi></addata></record> |
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| subjects | Applied and Technical Physics Atomic B spline functions Basis functions Complex Systems Condensed Matter Physics Initial conditions Korteweg-Devries equation Mathematical and Computational Physics Molecular Optical and Plasma Physics Physics Physics and Astronomy Regular Article Shallow water Solitary waves Theoretical Water waves |
| title | Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation |
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