Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions
In this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block method directly solves the second order IVPs. Likewise, the metho...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Science Publications
2017
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| Online Access: | https://repo.uum.edu.my/id/eprint/27948/1/AJAS%2014%202%202017%20309%20315.pdf |
| _version_ | 1825805720778440704 |
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| author | Adeyeye, Oluwaseun Omar, Zurni |
| author_facet | Adeyeye, Oluwaseun Omar, Zurni |
| author_sort | Adeyeye, Oluwaseun |
| collection | UUM |
| description | In this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block method directly solves the second order IVPs. Likewise, the methodology utilized also avoids the cumbersome steps involved in the widely adopted interpolation approach for developing hybrid block methods as a simple and easy to implement algorithm using the knowledge from the conventional Taylor series expansions with less cumbersome steps is introduced. To further justify the usability of this hybrid block method, the basic properties which will infer convergence when adopted to solve differential equations are investigated. The hybrid block method validates its superiority over existing methods as seen in the improved accuracy when solving the considered numerical examples. |
| first_indexed | 2024-07-04T06:36:53Z |
| format | Article |
| id | uum-27948 |
| institution | Universiti Utara Malaysia |
| language | English |
| last_indexed | 2024-07-04T06:36:53Z |
| publishDate | 2017 |
| publisher | Science Publications |
| record_format | eprints |
| spelling | uum-279482020-12-06T06:37:32Z https://repo.uum.edu.my/id/eprint/27948/ Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions Adeyeye, Oluwaseun Omar, Zurni QA75 Electronic computers. Computer science In this article, a hybrid block method is utilized for the numerical approximation of second order Initial Value Problems (IVPs). The rigor of reduction to a system of first order initial value problems is bypassed as the hybrid block method directly solves the second order IVPs. Likewise, the methodology utilized also avoids the cumbersome steps involved in the widely adopted interpolation approach for developing hybrid block methods as a simple and easy to implement algorithm using the knowledge from the conventional Taylor series expansions with less cumbersome steps is introduced. To further justify the usability of this hybrid block method, the basic properties which will infer convergence when adopted to solve differential equations are investigated. The hybrid block method validates its superiority over existing methods as seen in the improved accuracy when solving the considered numerical examples. Science Publications 2017 Article PeerReviewed application/pdf en https://repo.uum.edu.my/id/eprint/27948/1/AJAS%2014%202%202017%20309%20315.pdf Adeyeye, Oluwaseun and Omar, Zurni (2017) Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions. American Journal of Applied Sciences, 14 (2). pp. 309-315. ISSN 1546-9239 http://doi.org/10.3844/ajassp.2017.309.315 doi:10.3844/ajassp.2017.309.315 doi:10.3844/ajassp.2017.309.315 |
| spellingShingle | QA75 Electronic computers. Computer science Adeyeye, Oluwaseun Omar, Zurni Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions |
| title | Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions |
| title_full | Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions |
| title_fullStr | Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions |
| title_full_unstemmed | Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions |
| title_short | Hybrid block method for direct numerical approximation of second order initial value problems using Taylor Series Expansions |
| title_sort | hybrid block method for direct numerical approximation of second order initial value problems using taylor series expansions |
| topic | QA75 Electronic computers. Computer science |
| url | https://repo.uum.edu.my/id/eprint/27948/1/AJAS%2014%202%202017%20309%20315.pdf |
| work_keys_str_mv | AT adeyeyeoluwaseun hybridblockmethodfordirectnumericalapproximationofsecondorderinitialvalueproblemsusingtaylorseriesexpansions AT omarzurni hybridblockmethodfordirectnumericalapproximationofsecondorderinitialvalueproblemsusingtaylorseriesexpansions |