On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems
Second-order oscillatory problems have been found to be applicable in studying various phenomena in science and engineering; this is because these problems have the capabilities of replicating different aspects of the real world. In this research, a new hybrid method shall be formulated for the simu...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/282 |
| _version_ | 1797613510902939648 |
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| author | Lydia J. Kwari Joshua Sunday Joel N. Ndam Ali Shokri Yuanheng Wang |
| author_facet | Lydia J. Kwari Joshua Sunday Joel N. Ndam Ali Shokri Yuanheng Wang |
| author_sort | Lydia J. Kwari |
| collection | DOAJ |
| description | Second-order oscillatory problems have been found to be applicable in studying various phenomena in science and engineering; this is because these problems have the capabilities of replicating different aspects of the real world. In this research, a new hybrid method shall be formulated for the simulations of second-order oscillatory problems with applications to physical systems. The proposed method shall be formulated using the procedure of interpolation and collocation by adopting power series as basis function. In formulating the method, off-step points were introduced within the interval of integration in order to bypass the Dahlquist barrier, improve the accuracy of the method and also upgrade the order of consistence of the method. The paper further validated the some properties of the hybrid method derived and from the results obtained; the new method was found to be consistent, convergent and stable. The simulation results generated as a result of the application of the new method on some second-order oscillatory differential equations also showed that the new hybrid method is computationally reliable. |
| first_indexed | 2024-03-11T06:56:46Z |
| format | Article |
| id | doaj.art-ba9da2775b794caab78541a5f783bc22 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:56:46Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ba9da2775b794caab78541a5f783bc222023-11-17T09:35:20ZengMDPI AGAxioms2075-16802023-03-0112328210.3390/axioms12030282On the Simulations of Second-Order Oscillatory Problems with Applications to Physical SystemsLydia J. Kwari0Joshua Sunday1Joel N. Ndam2Ali Shokri3Yuanheng Wang4Department of Mathematics, School of Sciences, Federal College of Education, Pankshin 933105, NigeriaDepartment of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930003, NigeriaDepartment of Mathematics, Faculty of Natural Sciences, University of Jos, Jos 930003, NigeriaDepartment of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh 83111-55181, IranCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaSecond-order oscillatory problems have been found to be applicable in studying various phenomena in science and engineering; this is because these problems have the capabilities of replicating different aspects of the real world. In this research, a new hybrid method shall be formulated for the simulations of second-order oscillatory problems with applications to physical systems. The proposed method shall be formulated using the procedure of interpolation and collocation by adopting power series as basis function. In formulating the method, off-step points were introduced within the interval of integration in order to bypass the Dahlquist barrier, improve the accuracy of the method and also upgrade the order of consistence of the method. The paper further validated the some properties of the hybrid method derived and from the results obtained; the new method was found to be consistent, convergent and stable. The simulation results generated as a result of the application of the new method on some second-order oscillatory differential equations also showed that the new hybrid method is computationally reliable.https://www.mdpi.com/2075-1680/12/3/282hybrid methodconvergencedifferential equationoscillatory problemsphysical systems |
| spellingShingle | Lydia J. Kwari Joshua Sunday Joel N. Ndam Ali Shokri Yuanheng Wang On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems Axioms hybrid method convergence differential equation oscillatory problems physical systems |
| title | On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems |
| title_full | On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems |
| title_fullStr | On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems |
| title_full_unstemmed | On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems |
| title_short | On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems |
| title_sort | on the simulations of second order oscillatory problems with applications to physical systems |
| topic | hybrid method convergence differential equation oscillatory problems physical systems |
| url | https://www.mdpi.com/2075-1680/12/3/282 |
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