Hybrid one-step block fourth derivative method for the direct solution of third order initial value problems of ordinary differential equations
An efficient one step block method with generalized two-point-hybrid is developed for solving initial value problems of third order ordinary differential equations directly. In driving this algorithm, a power series approximate function is interpolated at {xn, xn+r, xn+s} while its third and fourth...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Academic Publications, Ltd.
2018
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| Subjects: | |
| Online Access: | https://repo.uum.edu.my/id/eprint/27940/1/HJPAM%20119%201%202018%20207%20224.pdf |
| Summary: | An efficient one step block method with generalized two-point-hybrid is developed for solving initial value problems of third order ordinary differential equations directly. In driving this algorithm, a power series approximate function is interpolated at {xn, xn+r, xn+s} while its third and fourth derivatives are collocated at all points {xn, xn+r, xn+s, xn+1} in the given interval. The proposed method is then tested for initial value problems of third order ordinary differential equations solved previously by other methods. The numerical results
confirm the superiority of the new method to the existing methods regarding accuracy. |
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