Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation
Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by oursel...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/891519 |
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| _version_ | 1832549318149537792 |
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| author | Dang Quang A. Nguyen Van Thien |
| author_facet | Dang Quang A. Nguyen Van Thien |
| author_sort | Dang Quang A. |
| collection | DOAJ |
| description | Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method. |
| format | Article |
| id | doaj-art-8e0bd5bf279240099f1c0127c1b4b6e1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-8e0bd5bf279240099f1c0127c1b4b6e12025-02-03T06:11:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/891519891519Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type EquationDang Quang A.0Nguyen Van Thien1Institute of Information Technology, VAST, 18 Hoang Quoc Viet, Cau Giay, Hanoi 10000, VietnamHanoi University of Industry, Minh Khai, Tu Liem, Hanoi 10000, VietnamSolving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.http://dx.doi.org/10.1155/2012/891519 |
| spellingShingle | Dang Quang A. Nguyen Van Thien Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation Journal of Applied Mathematics |
| title | Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation |
| title_full | Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation |
| title_fullStr | Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation |
| title_full_unstemmed | Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation |
| title_short | Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation |
| title_sort | iterative method for solving the second boundary value problem for biharmonic type equation |
| url | http://dx.doi.org/10.1155/2012/891519 |
| work_keys_str_mv | AT dangquanga iterativemethodforsolvingthesecondboundaryvalueproblemforbiharmonictypeequation AT nguyenvanthien iterativemethodforsolvingthesecondboundaryvalueproblemforbiharmonictypeequation |