Variational Estimation Methods for Sturm–Liouville Problems
In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/20/3728 |
| _version_ | 1797471720813101056 |
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| author | Elena Corina Cipu Cosmin Dănuţ Barbu |
| author_facet | Elena Corina Cipu Cosmin Dănuţ Barbu |
| author_sort | Elena Corina Cipu |
| collection | DOAJ |
| description | In this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (the variational equation associated through the Euler–Lagrange variational principle and Nehari’s method, shooting method and bisection method) and iterative variational methods (He’s method and HPM) for regular RSL are unitary presented in final part of the paper, which ends with applications. |
| first_indexed | 2024-03-09T19:52:13Z |
| format | Article |
| id | doaj.art-76de216ce8364de49b51c4c52b6ff0b3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T19:52:13Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-76de216ce8364de49b51c4c52b6ff0b32023-11-24T01:06:17ZengMDPI AGMathematics2227-73902022-10-011020372810.3390/math10203728Variational Estimation Methods for Sturm–Liouville ProblemsElena Corina Cipu0Cosmin Dănuţ Barbu1Department of Applied Mathematics, University Politehnica of Bucharest, Spl. Independentei, No. 313, RO-060042 Bucharest, RomaniaDepartment of Applied Mathematics, University Politehnica of Bucharest, Spl. Independentei, No. 313, RO-060042 Bucharest, RomaniaIn this paper, we are concerned with approach solutions for Sturm–Liouville problems (SLP) using variational problem (VP) formulation of regular SLP. The minimization problem (MP) is also set forth, and the connection between the solution of each formulation is then proved. Variational estimations (the variational equation associated through the Euler–Lagrange variational principle and Nehari’s method, shooting method and bisection method) and iterative variational methods (He’s method and HPM) for regular RSL are unitary presented in final part of the paper, which ends with applications.https://www.mdpi.com/2227-7390/10/20/3728BVP nonlinear problemsvariational methodsestimating nonlinearitiesGreen function |
| spellingShingle | Elena Corina Cipu Cosmin Dănuţ Barbu Variational Estimation Methods for Sturm–Liouville Problems Mathematics BVP nonlinear problems variational methods estimating nonlinearities Green function |
| title | Variational Estimation Methods for Sturm–Liouville Problems |
| title_full | Variational Estimation Methods for Sturm–Liouville Problems |
| title_fullStr | Variational Estimation Methods for Sturm–Liouville Problems |
| title_full_unstemmed | Variational Estimation Methods for Sturm–Liouville Problems |
| title_short | Variational Estimation Methods for Sturm–Liouville Problems |
| title_sort | variational estimation methods for sturm liouville problems |
| topic | BVP nonlinear problems variational methods estimating nonlinearities Green function |
| url | https://www.mdpi.com/2227-7390/10/20/3728 |
| work_keys_str_mv | AT elenacorinacipu variationalestimationmethodsforsturmliouvilleproblems AT cosmindanutbarbu variationalestimationmethodsforsturmliouvilleproblems |