A new modification of an iterative method based on inverse polynomial for solving Cauchy problems
AbstractThis paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on an inverse polynomial technique. The proposed method is proven to be consistent, stable, and convergent. We also demonstrate the consistency property of the One-stage scheme and the Tw...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2023.2228054 |
| _version_ | 1797793414359547904 |
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| author | Ali Hasan Ali Osama Alabdali Mustafa T. Yaseen Maryam Al-Kandari Omar Bazighifan |
| author_facet | Ali Hasan Ali Osama Alabdali Mustafa T. Yaseen Maryam Al-Kandari Omar Bazighifan |
| author_sort | Ali Hasan Ali |
| collection | DOAJ |
| description | AbstractThis paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on an inverse polynomial technique. The proposed method is proven to be consistent, stable, and convergent. We also demonstrate the consistency property of the One-stage scheme and the Two-stage scheme, as well as the stability property of the proposed method. To validate the accuracy of our approach, we conduct several numerical experiments and present the results graphically. Our findings show that the proposed method outperforms existing approaches in terms of accuracy and efficiency. Additionally, we discuss the implications of our results for future research in this field. Overall, this paper provides a valuable contribution to the numerical solution of IVPs and lays the groundwork for further exploration in this area. |
| first_indexed | 2024-03-13T02:47:56Z |
| format | Article |
| id | doaj.art-e63fe5370bc54808a0c6404d785aed79 |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-03-13T02:47:56Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-e63fe5370bc54808a0c6404d785aed792023-06-28T14:38:27ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992023-12-0130139340010.1080/25765299.2023.2228054A new modification of an iterative method based on inverse polynomial for solving Cauchy problemsAli Hasan Ali0Osama Alabdali1Mustafa T. Yaseen2Maryam Al-Kandari3Omar Bazighifan4Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, IraqDepartment of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, IraqDepartment of Business Administration, Shatt Al-Arab University College, Basra, IraqDepartment of Mathematics, Kuwait University, Khaldiyah City, KuwaitDepartment of Mathematics, Faculty of Science, Hadhramout University, Hadhramout, YemenAbstractThis paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on an inverse polynomial technique. The proposed method is proven to be consistent, stable, and convergent. We also demonstrate the consistency property of the One-stage scheme and the Two-stage scheme, as well as the stability property of the proposed method. To validate the accuracy of our approach, we conduct several numerical experiments and present the results graphically. Our findings show that the proposed method outperforms existing approaches in terms of accuracy and efficiency. Additionally, we discuss the implications of our results for future research in this field. Overall, this paper provides a valuable contribution to the numerical solution of IVPs and lays the groundwork for further exploration in this area.https://www.tandfonline.com/doi/10.1080/25765299.2023.2228054Approximationconvergencedifferential equationinitial value problemiterative method |
| spellingShingle | Ali Hasan Ali Osama Alabdali Mustafa T. Yaseen Maryam Al-Kandari Omar Bazighifan A new modification of an iterative method based on inverse polynomial for solving Cauchy problems Arab Journal of Basic and Applied Sciences Approximation convergence differential equation initial value problem iterative method |
| title | A new modification of an iterative method based on inverse polynomial for solving Cauchy problems |
| title_full | A new modification of an iterative method based on inverse polynomial for solving Cauchy problems |
| title_fullStr | A new modification of an iterative method based on inverse polynomial for solving Cauchy problems |
| title_full_unstemmed | A new modification of an iterative method based on inverse polynomial for solving Cauchy problems |
| title_short | A new modification of an iterative method based on inverse polynomial for solving Cauchy problems |
| title_sort | new modification of an iterative method based on inverse polynomial for solving cauchy problems |
| topic | Approximation convergence differential equation initial value problem iterative method |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2023.2228054 |
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