Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods
A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition (ADM), differential transform (DTM), least squares vector machines (LSSVMM), and multiple variational iteration (MVIM). A natural...
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Sakarya University
2023-12-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/3330050 |
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| _version_ | 1846111338294673408 |
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| author | Hasan Ömür Özer Birkan Durak Aziz Sezgin Lütfi Emir Sakman |
| author_facet | Hasan Ömür Özer Birkan Durak Aziz Sezgin Lütfi Emir Sakman |
| author_sort | Hasan Ömür Özer |
| collection | DOAJ |
| description | A large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition (ADM), differential transform (DTM), least squares vector machines (LSSVMM), and multiple variational iteration (MVIM). A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods. |
| format | Article |
| id | doaj-art-908160f129a34736a96fb8d2a070c0e0 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-908160f129a34736a96fb8d2a070c0e02024-12-23T08:15:45ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-12-012761345135410.16984/saufenbilder.134264528Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer MethodsHasan Ömür Özer0https://orcid.org/0000-0002-6388-4638Birkan Durak1https://orcid.org/0000-0002-8196-5407Aziz Sezgin2https://orcid.org/0000-0001-6861-5309Lütfi Emir Sakman3https://orcid.org/0000-0002-9599-8875İstanbul University-Cerrahpaşa, Vocational School of Technical Sciences, Department Of Electricity And Energy, Air Conditioning and Refrigeration Technology Pr.Istanbul University-Cerrahpaşa, Vocational School of Technical Sciences, Department of Motor Vehicles and Transportation Technologies, Aircraft Technology Pr.ISTANBUL UNIVERSITY-CERRAHPASA, FACULTY OF ENGINEERING, DEPARTMENT OF MECHANICAL ENGINEERING, DEPARTMENT OF AUTOMOTIVEISTANBUL UNIVERSITY-CERRAHPASA, FACULTY OF ENGINEERING, DEPARTMENT OF MECHANICAL ENGINEERING, DEPARTMENT OF THEORY AND DYNAMICS OF MACHINESA large variety of new methods are being developed for fast and efficient solutions of nonlinear boundary value problems. Some of these methods are, Adomian decomposition (ADM), differential transform (DTM), least squares vector machines (LSSVMM), and multiple variational iteration (MVIM). A natural question arises as to how efficient and simple to use these newer methods are compared to classical methods. One of the simplest and widely applicable classical methods is the collocation method. The overall performance of collocation method and the newer methods are compared on a number of problems, which were previously used to benchmark the newer methods. It is concluded that, at least for the problems considered, the collocation method performs as successfully as the newer methods.https://dergipark.org.tr/tr/download/article-file/3330050collocation methodnonlinear differential equationsboundary value problemsapproximate solution. |
| spellingShingle | Hasan Ömür Özer Birkan Durak Aziz Sezgin Lütfi Emir Sakman Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi collocation method nonlinear differential equations boundary value problems approximate solution. |
| title | Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods |
| title_full | Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods |
| title_fullStr | Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods |
| title_full_unstemmed | Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods |
| title_short | Approximate Solutions of Nonlinear Boundary Value Problems by Collocation Methods Compared to Newer Methods |
| title_sort | approximate solutions of nonlinear boundary value problems by collocation methods compared to newer methods |
| topic | collocation method nonlinear differential equations boundary value problems approximate solution. |
| url | https://dergipark.org.tr/tr/download/article-file/3330050 |
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