Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator
Solving nonlinear differential equation of a circular sector oscillator is of a scientific importance. Thus, to solve such equations, a single- step implicit block method involving one hybrid point with the introduction of a third derivative is proposed. To derive this method, the approximate basis...
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| Format: | Article |
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Springer
2020
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| author | Farhan, M. Omar, Zurni Mebarek-Oudina, F. Raza, J. Shah, Z. Choudhari, R. V Makinde, O. D. |
| author_facet | Farhan, M. Omar, Zurni Mebarek-Oudina, F. Raza, J. Shah, Z. Choudhari, R. V Makinde, O. D. |
| author_sort | Farhan, M. |
| collection | UUM |
| description | Solving nonlinear differential equation of a circular sector oscillator is of a scientific importance. Thus, to solve such equations, a single- step implicit block method involving one hybrid point with the introduction of a third derivative is proposed. To derive this method, the approximate basis solution is interpolated at {xn, xn + 3/5} while its second and third derivatives are collocated at all points {xn, xn + 3/5, xn + 1}on the integrated interval of approximation. Numerical results are presented in the form of table and graphs for the variation of different physical parameters. The study reveals that the proposed hybrid block method is zero stable, which proves that it is convergent beside a significant interval of absolute stability, thus making it suitable for solving stiff ODEs. |
| first_indexed | 2024-07-04T06:36:47Z |
| format | Article |
| id | uum-27918 |
| institution | Universiti Utara Malaysia |
| last_indexed | 2024-07-04T06:36:47Z |
| publishDate | 2020 |
| publisher | Springer |
| record_format | eprints |
| spelling | uum-279182020-11-30T00:33:37Z https://repo.uum.edu.my/id/eprint/27918/ Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator Farhan, M. Omar, Zurni Mebarek-Oudina, F. Raza, J. Shah, Z. Choudhari, R. V Makinde, O. D. QA75 Electronic computers. Computer science Solving nonlinear differential equation of a circular sector oscillator is of a scientific importance. Thus, to solve such equations, a single- step implicit block method involving one hybrid point with the introduction of a third derivative is proposed. To derive this method, the approximate basis solution is interpolated at {xn, xn + 3/5} while its second and third derivatives are collocated at all points {xn, xn + 3/5, xn + 1}on the integrated interval of approximation. Numerical results are presented in the form of table and graphs for the variation of different physical parameters. The study reveals that the proposed hybrid block method is zero stable, which proves that it is convergent beside a significant interval of absolute stability, thus making it suitable for solving stiff ODEs. Springer 2020 Article PeerReviewed Farhan, M. and Omar, Zurni and Mebarek-Oudina, F. and Raza, J. and Shah, Z. and Choudhari, R. V and Makinde, O. D. (2020) Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator. Computational Mathematics and Modeling, 31 (1). pp. 116-132. ISSN 1046-283X http://doi.org/10.1007/s10598-020-09480-0 doi:10.1007/s10598-020-09480-0 doi:10.1007/s10598-020-09480-0 |
| spellingShingle | QA75 Electronic computers. Computer science Farhan, M. Omar, Zurni Mebarek-Oudina, F. Raza, J. Shah, Z. Choudhari, R. V Makinde, O. D. Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator |
| title | Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator |
| title_full | Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator |
| title_fullStr | Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator |
| title_full_unstemmed | Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator |
| title_short | Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator |
| title_sort | implementation of the one step one hybrid block method on the nonlinear equation of a circular sector oscillator |
| topic | QA75 Electronic computers. Computer science |
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