Approximate solutions of the Fourth-Order Eigenvalue Problem
In this paper, the differential transformation (DTM) and the Adomian decomposition (ADM) methods are proposed for solving fourth order eigenvalue problem. This fourth order eigenvalue problem has nonstrongly regular boundary conditions. This the fourth order problem has been examined for p(t) = t, B...
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Çanakkale Onsekiz Mart University
2022-06-01
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| Series: | Journal of Advanced Research in Natural and Applied Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/1968592 |
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| author | Derya Arslan |
| author_facet | Derya Arslan |
| author_sort | Derya Arslan |
| collection | DOAJ |
| description | In this paper, the differential transformation (DTM) and the Adomian decomposition (ADM) methods are proposed for solving fourth order eigenvalue problem. This fourth order eigenvalue problem has nonstrongly regular boundary conditions. This the fourth order problem has been examined for p(t) = t, B = 0, a = 0,01 where p(t) ≠ 0 is a complex valued and a ≠ 0 The differential transformation and the Adomian decomposition methods are briefly described. An approximate solution is obtained by performing seven iterations with the Adomian decomposition method. The same number of iterations have been made in the differential transformation method. The approximation results obtained by both methods have been compared with each other. These data have been presented in table. The ADM and the DTM approximation solutions have been shown by plotting in Figure 1. Here, the approaches obtained by using the two methods are found to be in high agreement. Consequently, highly accurate approximate solutions of fourth order eigenvalue problem are obtained. Such good results also revealed that the Adomian decomposition and the differential transformation methods are fast, economical and motivating. The exact solution of the fourth order eigenvalue problem for nonstrongly regular can not be found in the literature. Therefore, this study will give an important idea to determine approximate solution behavior of this fourth order problem. |
| format | Article |
| id | doaj-art-87686cb20c984750b3d183318c712c44 |
| institution | Kabale University |
| issn | 2757-5195 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | Çanakkale Onsekiz Mart University |
| record_format | Article |
| series | Journal of Advanced Research in Natural and Applied Sciences |
| spelling | doaj-art-87686cb20c984750b3d183318c712c442025-02-05T17:58:10ZengÇanakkale Onsekiz Mart UniversityJournal of Advanced Research in Natural and Applied Sciences2757-51952022-06-018221422110.28979/jarnas.993943453Approximate solutions of the Fourth-Order Eigenvalue ProblemDerya Arslan0https://orcid.org/0000-0001-6138-0607BİTLİS EREN ÜNİVERSİTESİIn this paper, the differential transformation (DTM) and the Adomian decomposition (ADM) methods are proposed for solving fourth order eigenvalue problem. This fourth order eigenvalue problem has nonstrongly regular boundary conditions. This the fourth order problem has been examined for p(t) = t, B = 0, a = 0,01 where p(t) ≠ 0 is a complex valued and a ≠ 0 The differential transformation and the Adomian decomposition methods are briefly described. An approximate solution is obtained by performing seven iterations with the Adomian decomposition method. The same number of iterations have been made in the differential transformation method. The approximation results obtained by both methods have been compared with each other. These data have been presented in table. The ADM and the DTM approximation solutions have been shown by plotting in Figure 1. Here, the approaches obtained by using the two methods are found to be in high agreement. Consequently, highly accurate approximate solutions of fourth order eigenvalue problem are obtained. Such good results also revealed that the Adomian decomposition and the differential transformation methods are fast, economical and motivating. The exact solution of the fourth order eigenvalue problem for nonstrongly regular can not be found in the literature. Therefore, this study will give an important idea to determine approximate solution behavior of this fourth order problem.https://dergipark.org.tr/en/download/article-file/1968592fourth order eigen value problemapproximate solutionsnot strongly regular boundary conditionsadomian decomposition methoddifferential transform method |
| spellingShingle | Derya Arslan Approximate solutions of the Fourth-Order Eigenvalue Problem Journal of Advanced Research in Natural and Applied Sciences fourth order eigen value problem approximate solutions not strongly regular boundary conditions adomian decomposition method differential transform method |
| title | Approximate solutions of the Fourth-Order Eigenvalue Problem |
| title_full | Approximate solutions of the Fourth-Order Eigenvalue Problem |
| title_fullStr | Approximate solutions of the Fourth-Order Eigenvalue Problem |
| title_full_unstemmed | Approximate solutions of the Fourth-Order Eigenvalue Problem |
| title_short | Approximate solutions of the Fourth-Order Eigenvalue Problem |
| title_sort | approximate solutions of the fourth order eigenvalue problem |
| topic | fourth order eigen value problem approximate solutions not strongly regular boundary conditions adomian decomposition method differential transform method |
| url | https://dergipark.org.tr/en/download/article-file/1968592 |
| work_keys_str_mv | AT deryaarslan approximatesolutionsofthefourthordereigenvalueproblem |