The Shifted Vieta Pell solution in the calculus of variations via direct parameterization technique
In this article, a new parameterization direct method using Shifted Vieta Pell (SVP) functions is proposed to solve problems in the variation calculus. An explicit general formulation of operational matrix of derivative is obtained for the SVP functions and used to find an approximate solution for t...
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description | In this article, a new parameterization direct method using Shifted Vieta Pell (SVP) functions is proposed to solve problems in the variation calculus. An explicit general formulation of operational matrix of derivative is obtained for the SVP functions and used to find an approximate solution for the calculus of variation problem. The first step in our suggested method is to express the unknown variables in terms of the basis functions SVP with unknown coefficients. Then, the operation matrix of derivative and some important properties of the SVP functions are applied to achieve a nonlinear programming problem in terms of the unknown coefficients. Then the quadratic programming algorithm is used to calculate the unknown parameters. Two test numerical examples of different calculus of variation types are demonstrated together with approximate solutions for proving the accuracy and applicability of the suggested SVP method. |
doi_str_mv | 10.1063/5.0150746 |
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An explicit general formulation of operational matrix of derivative is obtained for the SVP functions and used to find an approximate solution for the calculus of variation problem. The first step in our suggested method is to express the unknown variables in terms of the basis functions SVP with unknown coefficients. Then, the operation matrix of derivative and some important properties of the SVP functions are applied to achieve a nonlinear programming problem in terms of the unknown coefficients. Then the quadratic programming algorithm is used to calculate the unknown parameters. Two test numerical examples of different calculus of variation types are demonstrated together with approximate solutions for proving the accuracy and applicability of the suggested SVP method.</description><identifier>ISSN: 0094-243X</identifier><identifier>EISSN: 1551-7616</identifier><identifier>DOI: 10.1063/5.0150746</identifier><identifier>CODEN: APCPCS</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Algorithms ; Basis functions ; Calculus of variations ; Derivatives ; Nonlinear programming ; Parameterization ; Quadratic programming</subject><ispartof>AIP Conference Proceedings, 2023, Vol.2820 (1)</ispartof><rights>Author(s)</rights><rights>2023 Author(s). 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An explicit general formulation of operational matrix of derivative is obtained for the SVP functions and used to find an approximate solution for the calculus of variation problem. The first step in our suggested method is to express the unknown variables in terms of the basis functions SVP with unknown coefficients. Then, the operation matrix of derivative and some important properties of the SVP functions are applied to achieve a nonlinear programming problem in terms of the unknown coefficients. Then the quadratic programming algorithm is used to calculate the unknown parameters. Two test numerical examples of different calculus of variation types are demonstrated together with approximate solutions for proving the accuracy and applicability of the suggested SVP method.</description><subject>Algorithms</subject><subject>Basis functions</subject><subject>Calculus of variations</subject><subject>Derivatives</subject><subject>Nonlinear programming</subject><subject>Parameterization</subject><subject>Quadratic programming</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2023</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNp9kEtLAzEUhYMoWKsL_0HAnTA1j0lmspTiCwoKFnEX0uSGpkw7Y5Ip6K93-gB3rs7ifPeew0HompIJJZLfiQmhglSlPEEjKgQtKknlKRoRosqClfzzHF2ktCKEqaqqR8jOl4Dfl8FncPgjQDb4DZoGp7bpc2g3OGxwHhBrGts3fcKtx1sTg9mZCW-DwS5EsBl3Jpo1ZIjhZ2_iDHa5CV89XKIzb5oEV0cdo_njw3z6XMxen16m97Oio7LOhTO-tNTVAF5KpbirqBPKCseY51J6s6COGUlNSaHiBBbCkoUHZgQ3BBQfo5vD2y62Q2rKetX2cTMkalYzJUpWKjpQtwcq2ZD3RXUXw9rEb71toxb6uJ_unP8PpkTvBv874L91sHQ4</recordid><startdate>20230626</startdate><enddate>20230626</enddate><creator>Khaleel, Inas Abd Ulkader</creator><creator>Shihab, Suha</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20230626</creationdate><title>The Shifted Vieta Pell solution in the calculus of variations via direct parameterization technique</title><author>Khaleel, Inas Abd Ulkader ; Shihab, Suha</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p168t-daf4c1d8eef66993d71d59c5d22f366fab1d2a61a41e730eb5c0bfe2a53a0e93</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Basis functions</topic><topic>Calculus of variations</topic><topic>Derivatives</topic><topic>Nonlinear programming</topic><topic>Parameterization</topic><topic>Quadratic programming</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Khaleel, Inas Abd Ulkader</creatorcontrib><creatorcontrib>Shihab, Suha</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Khaleel, Inas Abd Ulkader</au><au>Shihab, Suha</au><au>Raad, Haider</au><au>Link, Justin</au><au>Muayad TA, Mohammed</au><au>AL-Shmgani, Hanady</au><au>Al-Jadir, Thaer</au><au>McGrath, Sarah</au><au>Haider, Adawiya</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>The Shifted Vieta Pell solution in the calculus of variations via direct parameterization technique</atitle><btitle>AIP Conference Proceedings</btitle><date>2023-06-26</date><risdate>2023</risdate><volume>2820</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>In this article, a new parameterization direct method using Shifted Vieta Pell (SVP) functions is proposed to solve problems in the variation calculus. An explicit general formulation of operational matrix of derivative is obtained for the SVP functions and used to find an approximate solution for the calculus of variation problem. The first step in our suggested method is to express the unknown variables in terms of the basis functions SVP with unknown coefficients. Then, the operation matrix of derivative and some important properties of the SVP functions are applied to achieve a nonlinear programming problem in terms of the unknown coefficients. Then the quadratic programming algorithm is used to calculate the unknown parameters. Two test numerical examples of different calculus of variation types are demonstrated together with approximate solutions for proving the accuracy and applicability of the suggested SVP method.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/5.0150746</doi><tpages>9</tpages></addata></record> |
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subjects | Algorithms Basis functions Calculus of variations Derivatives Nonlinear programming Parameterization Quadratic programming |
title | The Shifted Vieta Pell solution in the calculus of variations via direct parameterization technique |
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