A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems
This paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic problems in ordinary differential equations (ODEs), the coefficients of which are independent of the frequency omega and step size h. This r...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/2343215 |
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| author | Mufutau Ajani Rufai Ali Shokri Ezekiel Olaoluwa Omole |
| author_facet | Mufutau Ajani Rufai Ali Shokri Ezekiel Olaoluwa Omole |
| author_sort | Mufutau Ajani Rufai |
| collection | DOAJ |
| description | This paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic problems in ordinary differential equations (ODEs), the coefficients of which are independent of the frequency omega and step size h. This research is significant because it has numerous applications to real-life phenomena such as chaotic dynamical systems, almost periodic problems, and duffing equations. The current method is derived from the collocation of a derivative function at the equidistant grid and off-grid points. The TDHMT obtained is a continuous scheme for obtaining simultaneous approximations to the solution and its derivative at each point in the x0,xN interval integration. The presence of high derivatives increases the order of the method, which increases the accuracy method’s order and the stability property, as discussed in detail. Finally, the proposed method is compared to existing methods in the literature on some oscillatory and periodic test problems to demonstrate the technique’s effectiveness and productivity. |
| format | Article |
| id | doaj-art-06d909217a2e4a71a992bfbe55309a53 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-06d909217a2e4a71a992bfbe55309a532025-02-03T01:29:53ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/2343215A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic ProblemsMufutau Ajani Rufai0Ali Shokri1Ezekiel Olaoluwa Omole2Dipartimento di MatematicaFaculty of Mathematical SciencesDepartment of Mathematics and StatisticsThis paper describes a third-derivative hybrid multistep technique (TDHMT) for solving second-order initial-value problems (IVPs) with oscillatory and periodic problems in ordinary differential equations (ODEs), the coefficients of which are independent of the frequency omega and step size h. This research is significant because it has numerous applications to real-life phenomena such as chaotic dynamical systems, almost periodic problems, and duffing equations. The current method is derived from the collocation of a derivative function at the equidistant grid and off-grid points. The TDHMT obtained is a continuous scheme for obtaining simultaneous approximations to the solution and its derivative at each point in the x0,xN interval integration. The presence of high derivatives increases the order of the method, which increases the accuracy method’s order and the stability property, as discussed in detail. Finally, the proposed method is compared to existing methods in the literature on some oscillatory and periodic test problems to demonstrate the technique’s effectiveness and productivity.http://dx.doi.org/10.1155/2023/2343215 |
| spellingShingle | Mufutau Ajani Rufai Ali Shokri Ezekiel Olaoluwa Omole A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems Journal of Mathematics |
| title | A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems |
| title_full | A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems |
| title_fullStr | A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems |
| title_full_unstemmed | A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems |
| title_short | A One-Point Third-Derivative Hybrid Multistep Technique for Solving Second-Order Oscillatory and Periodic Problems |
| title_sort | one point third derivative hybrid multistep technique for solving second order oscillatory and periodic problems |
| url | http://dx.doi.org/10.1155/2023/2343215 |
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