Derivation of a single-step hybrid block method with generalized two off-step points for solving second order ordinary differential equation directly
This paper proposes a single-step hybrid block method with generalized two off-step point for the direct solution of initial value problem of second order ordinary differential equations.The uses of power series approximate solution as an interpolation polynomial at the off points is employed in dev...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
North Atlantic University Union (NAUN)
2016
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| Subjects: | |
| Online Access: | http://repo.uum.edu.my/22310/1/IJMCS%2010%202016%20171-179.pdf http://repo.uum.edu.my/22310/ http://www.naun.org/cms.action?id=12110 |
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| Summary: | This paper proposes a single-step hybrid block method with generalized two off-step point for the direct solution of initial value problem of second order ordinary differential equations.The uses of power series approximate solution as an interpolation polynomial at the off points is employed in developing this method, while its second derivative is collocated at all points in the interval.Furthermore, some basic properties of the generalized method such as order, zero stability, consistency and convergence are also established. In addition, two examples of specific points of the developed method are considered to solve some initial value problems of second order ordinary differential equations. The numerical results confirm that the proposed method produces better accuracy if compared with the existing methods. |
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