Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method
Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/4925914 |
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| author | Oluwaseun Adeyeye Zurni Omar |
| author_facet | Oluwaseun Adeyeye Zurni Omar |
| author_sort | Oluwaseun Adeyeye |
| collection | DOAJ |
| description | Nonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A m+1th-step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where m is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at m+1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the m+1th-step block method was displayed in the solution for magnetohydrodynamic squeezing flow in porous medium. |
| format | Article |
| id | doaj-art-3f30d901b25d47b78e351fca528c80b8 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-3f30d901b25d47b78e351fca528c80b82025-02-03T06:11:42ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/49259144925914Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block MethodOluwaseun Adeyeye0Zurni Omar1Mathematics Department, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah, MalaysiaMathematics Department, School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Kedah, MalaysiaNonlinear boundary value problems (BVPs) are more tedious to solve than their linear counterparts. This is observed in the extra computation required when determining the missing conditions in transforming BVPs to initial value problems. Although a number of numerical approaches are already existent in literature to solve nonlinear BVPs, this article presents a new block method with improved accuracy to solve nonlinear BVPs. A m+1th-step block method is developed using a modified Taylor series approach to directly solve fourth-order nonlinear boundary value problems (BVPs) where m is the order of the differential equation under consideration. The schemes obtained were combined to simultaneously produce solution to the fourth-order nonlinear BVPs at m+1 points iteratively. The derived block method showed improved accuracy in comparison to previously existing authors when solving the same problems. In addition, the suitability of the m+1th-step block method was displayed in the solution for magnetohydrodynamic squeezing flow in porous medium.http://dx.doi.org/10.1155/2017/4925914 |
| spellingShingle | Oluwaseun Adeyeye Zurni Omar Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method International Journal of Differential Equations |
| title | Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method |
| title_full | Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method |
| title_fullStr | Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method |
| title_full_unstemmed | Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method |
| title_short | Solving Nonlinear Fourth-Order Boundary Value Problems Using a Numerical Approach: (m+1)th-Step Block Method |
| title_sort | solving nonlinear fourth order boundary value problems using a numerical approach m 1 th step block method |
| url | http://dx.doi.org/10.1155/2017/4925914 |
| work_keys_str_mv | AT oluwaseunadeyeye solvingnonlinearfourthorderboundaryvalueproblemsusinganumericalapproachm1thstepblockmethod AT zurniomar solvingnonlinearfourthorderboundaryvalueproblemsusinganumericalapproachm1thstepblockmethod |