Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems
© 2017, The Author(s). The multilevel augmentation method with the anti-derivatives of the Daubechies wavelets is presented for solving nonlinear two-point boundary value problems. The anti-derivatives of the Daubechies wavelets are applied as the multilevel bases for the subspaces of approximate so...
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th-cmuir.6653943832-400402017-09-28T03:38:04Z Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems Utudee S. Maleewong M. © 2017, The Author(s). The multilevel augmentation method with the anti-derivatives of the Daubechies wavelets is presented for solving nonlinear two-point boundary value problems. The anti-derivatives of the Daubechies wavelets are applied as the multilevel bases for the subspaces of approximate solutions. This process results in a full nonlinear system that can be solved by the multilevel augmentation method for reducing computational cost. The convergence rate of the present method is shown. It is the order of 2 s , 0 ≤ s≤ p when p is the order of the Daubechies wavelets. Various examples of the Dirichlet boundary conditions are shown to confirm the theoretical results. 2017-09-28T03:38:04Z 2017-09-28T03:38:04Z 1 Journal 16871839 2-s2.0-85017020981 10.1186/s13662-017-1156-8 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85017020981&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40040 |
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© 2017, The Author(s). The multilevel augmentation method with the anti-derivatives of the Daubechies wavelets is presented for solving nonlinear two-point boundary value problems. The anti-derivatives of the Daubechies wavelets are applied as the multilevel bases for the subspaces of approximate solutions. This process results in a full nonlinear system that can be solved by the multilevel augmentation method for reducing computational cost. The convergence rate of the present method is shown. It is the order of 2 s , 0 ≤ s≤ p when p is the order of the Daubechies wavelets. Various examples of the Dirichlet boundary conditions are shown to confirm the theoretical results. |
| format |
Journal |
| author |
Utudee S. Maleewong M. |
| spellingShingle |
Utudee S. Maleewong M. Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| author_facet |
Utudee S. Maleewong M. |
| author_sort |
Utudee S. |
| title |
Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| title_short |
Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| title_full |
Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| title_fullStr |
Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| title_full_unstemmed |
Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| title_sort |
multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems |
| publishDate |
2017 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85017020981&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40040 |
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