Haar wavelet collocation method for the numerical solution of singular initial value problems
In this paper, numerical solutions of singular initial value problems are obtained by the Haar wavelet collocation method (HWCM). The HWCM is a numerical method for solving integral equations, ordinary and partial differential equations. To show the efficiency of the HWCM, some examples are presente...
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| Format: | Article |
| Language: | English |
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Elsevier
2016-06-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447915000982 |
| _version_ | 1818669475538403328 |
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| author | S.C. Shiralashetti A.B. Deshi P.B. Mutalik Desai |
| author_facet | S.C. Shiralashetti A.B. Deshi P.B. Mutalik Desai |
| author_sort | S.C. Shiralashetti |
| collection | DOAJ |
| description | In this paper, numerical solutions of singular initial value problems are obtained by the Haar wavelet collocation method (HWCM). The HWCM is a numerical method for solving integral equations, ordinary and partial differential equations. To show the efficiency of the HWCM, some examples are presented. This method provides a fast convergent series of easily computable components. The errors of HWCM are also computed. Through this analysis, the solution is found on the coarse grid points and then converging toward higher accuracy by increasing the level of the Haar wavelet. Comparisons with exact and existing numerical methods (adomian decomposition method (ADM) & variational iteration method (VIM)) solutions show that the HWCM is a powerful numerical method for the solution of the linear and non-linear singular initial value problems. The Haar wavelet adaptive grid method (HWAGM) based solutions show the excellent performance for the proposed problems. |
| first_indexed | 2024-12-17T06:52:48Z |
| format | Article |
| id | doaj.art-d88ede2c7fa14f8ab379126e090ce5e8 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-17T06:52:48Z |
| publishDate | 2016-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-d88ede2c7fa14f8ab379126e090ce5e82022-12-21T21:59:32ZengElsevierAin Shams Engineering Journal2090-44792016-06-017266367010.1016/j.asej.2015.06.006Haar wavelet collocation method for the numerical solution of singular initial value problemsS.C. Shiralashetti0A.B. Deshi1P.B. Mutalik Desai2P.G. Department of Studies in Mathematics, Karnatak University, Dharwad 580003, IndiaP.G. Department of Studies in Mathematics, Karnatak University, Dharwad 580003, IndiaDepartment of Mathematics, K.L.E. College of Engg. & Technology, Chikodi 591201, IndiaIn this paper, numerical solutions of singular initial value problems are obtained by the Haar wavelet collocation method (HWCM). The HWCM is a numerical method for solving integral equations, ordinary and partial differential equations. To show the efficiency of the HWCM, some examples are presented. This method provides a fast convergent series of easily computable components. The errors of HWCM are also computed. Through this analysis, the solution is found on the coarse grid points and then converging toward higher accuracy by increasing the level of the Haar wavelet. Comparisons with exact and existing numerical methods (adomian decomposition method (ADM) & variational iteration method (VIM)) solutions show that the HWCM is a powerful numerical method for the solution of the linear and non-linear singular initial value problems. The Haar wavelet adaptive grid method (HWAGM) based solutions show the excellent performance for the proposed problems.http://www.sciencedirect.com/science/article/pii/S2090447915000982Haar wavelet collocation methodSingular initial value problemsAdomian decomposition methodVariational iteration method |
| spellingShingle | S.C. Shiralashetti A.B. Deshi P.B. Mutalik Desai Haar wavelet collocation method for the numerical solution of singular initial value problems Ain Shams Engineering Journal Haar wavelet collocation method Singular initial value problems Adomian decomposition method Variational iteration method |
| title | Haar wavelet collocation method for the numerical solution of singular initial value problems |
| title_full | Haar wavelet collocation method for the numerical solution of singular initial value problems |
| title_fullStr | Haar wavelet collocation method for the numerical solution of singular initial value problems |
| title_full_unstemmed | Haar wavelet collocation method for the numerical solution of singular initial value problems |
| title_short | Haar wavelet collocation method for the numerical solution of singular initial value problems |
| title_sort | haar wavelet collocation method for the numerical solution of singular initial value problems |
| topic | Haar wavelet collocation method Singular initial value problems Adomian decomposition method Variational iteration method |
| url | http://www.sciencedirect.com/science/article/pii/S2090447915000982 |
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