An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method
We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30132/ http://psasir.upm.edu.my/id/eprint/30132/1/An%20efficient%20approach%20for%20solving%20nonlinear%20troesch.pdf |
| _version_ | 1848846591482396672 |
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| author | Nasab, A. Kazemi Atabakan, Z. Pashazadeh Kilicman, Adem |
| author_facet | Nasab, A. Kazemi Atabakan, Z. Pashazadeh Kilicman, Adem |
| author_sort | Nasab, A. Kazemi |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given to validate the efficiency and accuracy of the proposed technique. We compare the results with those ones reported in the literature in order to demonstrate that the method converges rapidly and approximates the exact solution very accurately by using only a small number of Chebyshev wavelet basis functions. Convergence analysis is also included. |
| first_indexed | 2025-11-15T09:05:09Z |
| format | Article |
| id | upm-30132 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T09:05:09Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301322015-12-08T03:31:28Z http://psasir.upm.edu.my/id/eprint/30132/ An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method Nasab, A. Kazemi Atabakan, Z. Pashazadeh Kilicman, Adem We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given to validate the efficiency and accuracy of the proposed technique. We compare the results with those ones reported in the literature in order to demonstrate that the method converges rapidly and approximates the exact solution very accurately by using only a small number of Chebyshev wavelet basis functions. Convergence analysis is also included. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30132/1/An%20efficient%20approach%20for%20solving%20nonlinear%20troesch.pdf Nasab, A. Kazemi and Atabakan, Z. Pashazadeh and Kilicman, Adem (2013) An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method. Mathematical Problems in Engineering, 2013. art. no. 825817. pp. 1-10. ISSN 1024-123X http://www.hindawi.com/journals/mpe/2013/825817/ref/ 10.1155/2013/825817 English |
| spellingShingle | Nasab, A. Kazemi Atabakan, Z. Pashazadeh Kilicman, Adem An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| title | An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| title_full | An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| title_fullStr | An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| title_full_unstemmed | An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| title_short | An efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| title_sort | efficient approach for solving nonlinear troesch's and bratu's problems by wavelet analysis method |
| url | http://psasir.upm.edu.my/id/eprint/30132/ http://psasir.upm.edu.my/id/eprint/30132/ http://psasir.upm.edu.my/id/eprint/30132/ http://psasir.upm.edu.my/id/eprint/30132/1/An%20efficient%20approach%20for%20solving%20nonlinear%20troesch.pdf |