Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences
Symmetries are important in studying the dynamics of physical systems which in turn are converted to solve equations. Jarratt’s method and its variants have been used extensively for this purpose. That is why in the present study, a unified local convergence analysis is developed of higher order Jar...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/7/1162 |
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| author | Ramandeep Behl Ioannis K. Argyros Fouad Othman Mallawi Christopher I. Argyros |
| author_facet | Ramandeep Behl Ioannis K. Argyros Fouad Othman Mallawi Christopher I. Argyros |
| author_sort | Ramandeep Behl |
| collection | DOAJ |
| description | Symmetries are important in studying the dynamics of physical systems which in turn are converted to solve equations. Jarratt’s method and its variants have been used extensively for this purpose. That is why in the present study, a unified local convergence analysis is developed of higher order Jarratt-type schemes for equations given on Banach space. Such schemes have been studied on the multidimensional Euclidean space provided that high order derivatives (not appearing on the schemes) exist. In addition, no errors estimates or results on the uniqueness of the solution that can be computed are given. These problems restrict the applicability of the methods. We address all these problems by using the first order derivative (appearing only on the schemes). Hence, the region of applicability of existing schemes is enlarged. Our technique can be used on other methods due to its generality. Numerical experiments from chemistry and other disciplines of applied sciences complete this study. |
| first_indexed | 2024-03-10T09:59:42Z |
| format | Article |
| id | doaj.art-6f7d747ddd24401da3825bbe2929c1d5 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T09:59:42Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6f7d747ddd24401da3825bbe2929c1d52023-11-22T02:01:55ZengMDPI AGSymmetry2073-89942021-06-01137116210.3390/sym13071162Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied SciencesRamandeep Behl0Ioannis K. Argyros1Fouad Othman Mallawi2Christopher I. Argyros3Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Computer Science, University of Oklahoma, Norman, OK 73071, USASymmetries are important in studying the dynamics of physical systems which in turn are converted to solve equations. Jarratt’s method and its variants have been used extensively for this purpose. That is why in the present study, a unified local convergence analysis is developed of higher order Jarratt-type schemes for equations given on Banach space. Such schemes have been studied on the multidimensional Euclidean space provided that high order derivatives (not appearing on the schemes) exist. In addition, no errors estimates or results on the uniqueness of the solution that can be computed are given. These problems restrict the applicability of the methods. We address all these problems by using the first order derivative (appearing only on the schemes). Hence, the region of applicability of existing schemes is enlarged. Our technique can be used on other methods due to its generality. Numerical experiments from chemistry and other disciplines of applied sciences complete this study.https://www.mdpi.com/2073-8994/13/7/1162Jarratt-type schemesBanach spaceorder of convergencesystem of nonlinear equations |
| spellingShingle | Ramandeep Behl Ioannis K. Argyros Fouad Othman Mallawi Christopher I. Argyros Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences Symmetry Jarratt-type schemes Banach space order of convergence system of nonlinear equations |
| title | Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences |
| title_full | Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences |
| title_fullStr | Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences |
| title_full_unstemmed | Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences |
| title_short | Convergence of Higher Order Jarratt-Type Schemes for Nonlinear Equations from Applied Sciences |
| title_sort | convergence of higher order jarratt type schemes for nonlinear equations from applied sciences |
| topic | Jarratt-type schemes Banach space order of convergence system of nonlinear equations |
| url | https://www.mdpi.com/2073-8994/13/7/1162 |
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