Three-Step Block Method for Solving Nonlinear Boundary Value Problems
We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary cond...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/379829 |
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| _version_ | 1832550240990789632 |
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| author | Phang Pei See Zanariah Abdul Majid Mohamed Suleiman |
| author_facet | Phang Pei See Zanariah Abdul Majid Mohamed Suleiman |
| author_sort | Phang Pei See |
| collection | DOAJ |
| description | We propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method. |
| format | Article |
| id | doaj-art-c4b4515bec0142ed82c505258d0e68c0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c4b4515bec0142ed82c505258d0e68c02025-02-03T06:07:26ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/379829379829Three-Step Block Method for Solving Nonlinear Boundary Value ProblemsPhang Pei See0Zanariah Abdul Majid1Mohamed Suleiman2Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaWe propose a three-step block method of Adam’s type to solve nonlinear second-order two-point boundary value problems of Dirichlet type and Neumann type directly. We also extend this method to solve the system of second-order boundary value problems which have the same or different two boundary conditions. The method will be implemented in predictor corrector mode and obtain the approximate solutions at three points simultaneously using variable step size strategy. The proposed block method will be adapted with multiple shooting techniques via the three-step iterative method. The boundary value problem will be solved without reducing to first-order equations. The numerical results are presented to demonstrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2014/379829 |
| spellingShingle | Phang Pei See Zanariah Abdul Majid Mohamed Suleiman Three-Step Block Method for Solving Nonlinear Boundary Value Problems Abstract and Applied Analysis |
| title | Three-Step Block Method for Solving Nonlinear Boundary Value Problems |
| title_full | Three-Step Block Method for Solving Nonlinear Boundary Value Problems |
| title_fullStr | Three-Step Block Method for Solving Nonlinear Boundary Value Problems |
| title_full_unstemmed | Three-Step Block Method for Solving Nonlinear Boundary Value Problems |
| title_short | Three-Step Block Method for Solving Nonlinear Boundary Value Problems |
| title_sort | three step block method for solving nonlinear boundary value problems |
| url | http://dx.doi.org/10.1155/2014/379829 |
| work_keys_str_mv | AT phangpeisee threestepblockmethodforsolvingnonlinearboundaryvalueproblems AT zanariahabdulmajid threestepblockmethodforsolvingnonlinearboundaryvalueproblems AT mohamedsuleiman threestepblockmethodforsolvingnonlinearboundaryvalueproblems |