A rational approximation based on Bernstein polynomials for high order initial and boundary values problems
We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is dif...
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| Veröffentlicht in: | Applied mathematics and computation 2011-07, Vol.217 (22), p.9438-9450 |
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| container_title | Applied mathematics and computation |
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| creator | Işik, Osman Raşit Sezer, Mehmet Güney, Zekeriya |
| description | We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann
[1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution
f
∈
C
d+2
[
a,
b]. |
| doi_str_mv | 10.1016/j.amc.2011.04.038 |
| format | Article |
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[1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution
f
∈
C
d+2
[
a,
b].</description><identifier>ISSN: 0096-3003</identifier><identifier>EISSN: 1873-5649</identifier><identifier>DOI: 10.1016/j.amc.2011.04.038</identifier><identifier>CODEN: AMHCBQ</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Approximate solution ; Approximation ; Approximations and expansions ; Bernstein polynomials ; Collocation method ; Collocation methods ; Construction ; Differential equations ; Exact sciences and technology ; Interpolation ; Mathematical analysis ; Mathematical models ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Partial differential equations ; Partial differential equations, boundary value problems ; Partial differential equations, initial value problems and time-dependant initial-boundary value problems ; Poles ; Rational interpolation ; Sciences and techniques of general use</subject><ispartof>Applied mathematics and computation, 2011-07, Vol.217 (22), p.9438-9450</ispartof><rights>2011 Elsevier Inc.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-d9055c2676e2b4c54ef68c9dd5f49225e8a69fae6d5510fae33038042caccf933</citedby><cites>FETCH-LOGICAL-c359t-d9055c2676e2b4c54ef68c9dd5f49225e8a69fae6d5510fae33038042caccf933</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0096300311005959$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24231116$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Işik, Osman Raşit</creatorcontrib><creatorcontrib>Sezer, Mehmet</creatorcontrib><creatorcontrib>Güney, Zekeriya</creatorcontrib><title>A rational approximation based on Bernstein polynomials for high order initial and boundary values problems</title><title>Applied mathematics and computation</title><description>We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann
[1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution
f
∈
C
d+2
[
a,
b].</description><subject>Approximate solution</subject><subject>Approximation</subject><subject>Approximations and expansions</subject><subject>Bernstein polynomials</subject><subject>Collocation method</subject><subject>Collocation methods</subject><subject>Construction</subject><subject>Differential equations</subject><subject>Exact sciences and technology</subject><subject>Interpolation</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Partial differential equations</subject><subject>Partial differential equations, boundary value problems</subject><subject>Partial differential equations, initial value problems and time-dependant initial-boundary value problems</subject><subject>Poles</subject><subject>Rational interpolation</subject><subject>Sciences and techniques of general use</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9UEtvEzEQthBIhMIP4OYL4rTb8TNrcSpVX1KlXuBsOfYsddi1g72pyL-vQyqOPc2M9D3m-wj5zKBnwPT5tnez7zkw1oPsQQxvyIoNa9EpLc1bsgIwuhMA4j35UOsWANaayRX5fUGLW2JObqJutyv5b5z_3XTjKgbalu9YUl0wJrrL0yHlObqp0jEX-hh_PdJcAhYaU1ziUSMFusn7FFw50Cc37bHSprqZcK4fybuxUfHTyzwjP6-vflzedvcPN3eXF_edF8osXTCglOd6rZFvpFcSRz14E4IapeFc4eC0GR3qoBSDtgjR8oLk3nk_GiHOyNeTbjP-0x5Y7Byrx2lyCfO-2mEwkg2Mq4ZkJ6QvudaCo92Vlr8cLAN77NVubevVHnu1IG3zaZwvL-quejeNxSUf638il1wwxnTDfTvhsEV9ilhs9RGTxxAL-sWGHF9xeQbQzI81</recordid><startdate>20110715</startdate><enddate>20110715</enddate><creator>Işik, Osman Raşit</creator><creator>Sezer, Mehmet</creator><creator>Güney, Zekeriya</creator><general>Elsevier Inc</general><general>Elsevier</general><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>20110715</creationdate><title>A rational approximation based on Bernstein polynomials for high order initial and boundary values problems</title><author>Işik, Osman Raşit ; Sezer, Mehmet ; Güney, Zekeriya</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-d9055c2676e2b4c54ef68c9dd5f49225e8a69fae6d5510fae33038042caccf933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Approximate solution</topic><topic>Approximation</topic><topic>Approximations and expansions</topic><topic>Bernstein polynomials</topic><topic>Collocation method</topic><topic>Collocation methods</topic><topic>Construction</topic><topic>Differential equations</topic><topic>Exact sciences and technology</topic><topic>Interpolation</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Partial differential equations</topic><topic>Partial differential equations, boundary value problems</topic><topic>Partial differential equations, initial value problems and time-dependant initial-boundary value problems</topic><topic>Poles</topic><topic>Rational interpolation</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Işik, Osman Raşit</creatorcontrib><creatorcontrib>Sezer, Mehmet</creatorcontrib><creatorcontrib>Güney, Zekeriya</creatorcontrib><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>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Işik, Osman Raşit</au><au>Sezer, Mehmet</au><au>Güney, Zekeriya</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A rational approximation based on Bernstein polynomials for high order initial and boundary values problems</atitle><jtitle>Applied mathematics and computation</jtitle><date>2011-07-15</date><risdate>2011</risdate><volume>217</volume><issue>22</issue><spage>9438</spage><epage>9450</epage><pages>9438-9450</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><coden>AMHCBQ</coden><abstract>We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann
[1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution
f
∈
C
d+2
[
a,
b].</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.amc.2011.04.038</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0096-3003 |
| ispartof | Applied mathematics and computation, 2011-07, Vol.217 (22), p.9438-9450 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Approximate solution Approximation Approximations and expansions Bernstein polynomials Collocation method Collocation methods Construction Differential equations Exact sciences and technology Interpolation Mathematical analysis Mathematical models Mathematics Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Poles Rational interpolation Sciences and techniques of general use |
| title | A rational approximation based on Bernstein polynomials for high order initial and boundary values problems |
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