Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method
In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation....
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| Veröffentlicht in: | Numerical methods for partial differential equations 2021-03, Vol.37 (2), p.1449-1463 |
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| container_title | Numerical methods for partial differential equations |
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| creator | Pedram, Leila Rostamy, Davoud |
| description | In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures. |
| doi_str_mv | 10.1002/num.22590 |
| format | Article |
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We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. 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We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures.</description><subject>Basis functions</subject><subject>Boundary value problems</subject><subject>B‐spline</subject><subject>conformable derivative</subject><subject>error estimate</subject><subject>Exact solutions</subject><subject>Finite element analysis</subject><subject>Finite element method</subject><subject>Korteweg-Devries equation</subject><subject>Korteweg‐de Vries equation</subject><subject>nonhomogeneous partial differential equation</subject><subject>Nonlinear equations</subject><issn>0749-159X</issn><issn>1098-2426</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQhS0EEqWw4AaWWLFIaztNEy9RxZ8oZUMRu8hJxq2rJG79Q9UdR-AAnI6T4LRsWY0075v3NA-hS0oGlBA2bH0zYCzh5Aj1KOFZxEZsfIx6JB3xiCb8_RSdWbsihNKE8h76nvkGjCpFja2uvVO6tVhL7JaAVaucCkKhfVsJs8MfovaA10YXNTRYarPH1mCcNwVUuNRtWDYiyNipBvCTNg62sPj5_KoAvxkFFsPGiy4GFzvsrWoXexPZhQGGYAytww24pa7O0YkUtYWLv9lH87vb18lDNH25f5zcTKOS8ZREkiSSCz6mcQYFLxlkNB1lFGgBVMSyLMmYxEUlYghglWRlwWAkqhQISMLGadxHVwff8NrGg3X5SnvThsicBaOM84x11PWBKo221oDM10Y1oZeckrwrPw_l5_vyAzs8sFtVw-5_MJ_Nnw8Xv9idi5o</recordid><startdate>202103</startdate><enddate>202103</enddate><creator>Pedram, Leila</creator><creator>Rostamy, Davoud</creator><general>John Wiley & Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-9585-8904</orcidid></search><sort><creationdate>202103</creationdate><title>Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method</title><author>Pedram, Leila ; Rostamy, Davoud</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2970-f05f9a96138eb9c2e817481e1be1a3fcc0603bda3e05fd58cb2e4ad7e0ef02673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Basis functions</topic><topic>Boundary value problems</topic><topic>B‐spline</topic><topic>conformable derivative</topic><topic>error estimate</topic><topic>Exact solutions</topic><topic>Finite element analysis</topic><topic>Finite element method</topic><topic>Korteweg-Devries equation</topic><topic>Korteweg‐de Vries equation</topic><topic>nonhomogeneous partial differential equation</topic><topic>Nonlinear equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pedram, Leila</creatorcontrib><creatorcontrib>Rostamy, Davoud</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>Aerospace 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>Numerical methods for partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pedram, Leila</au><au>Rostamy, Davoud</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method</atitle><jtitle>Numerical methods for partial differential equations</jtitle><date>2021-03</date><risdate>2021</risdate><volume>37</volume><issue>2</issue><spage>1449</spage><epage>1463</epage><pages>1449-1463</pages><issn>0749-159X</issn><eissn>1098-2426</eissn><abstract>In this paper, we investigate the initial‐boundary‐value problem for the nonhomogeneous Korteweg‐de Vries equation with conformable derivative on time part of it. We use the finite element method with B‐spline as the basis functions for obtaining the numerical solutions for this nonlinear equation. In addition, we prove a posteriori and a priori errors for it. These show the adaptivity and convergence of our method. Also, a posteriori error estimate concludes that the error estimate decreases as α increases. We show the accuracy of our work by comparing with the exact solution for the homogeneous KdV equation. We also bring an example for the nonhomogeneous conformable time KdV equation to demonstrate the accuracy and efficiency of the proposed method. Also, these numerical results are consistent with the result of theorems. The numerical results are given in tables and figures.</abstract><cop>Hoboken, USA</cop><pub>John Wiley & Sons, Inc</pub><doi>10.1002/num.22590</doi><tpages>29</tpages><orcidid>https://orcid.org/0000-0001-9585-8904</orcidid></addata></record> |
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| language | eng |
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| subjects | Basis functions Boundary value problems B‐spline conformable derivative error estimate Exact solutions Finite element analysis Finite element method Korteweg-Devries equation Korteweg‐de Vries equation nonhomogeneous partial differential equation Nonlinear equations |
| title | Numerical solutions of the initial boundary value problem for the perturbed conformable time Korteweg‐de Vries equation by using the finite element method |
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