An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations
Finding higher-order optimal derivative-free methods for multiple roots <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>m</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></semantics&...
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| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1809 |
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| author | Ramandeep Behl Samaher Khalaf Alharbi Fouad Othman Mallawi Mehdi Salimi |
| author_facet | Ramandeep Behl Samaher Khalaf Alharbi Fouad Othman Mallawi Mehdi Salimi |
| author_sort | Ramandeep Behl |
| collection | DOAJ |
| description | Finding higher-order optimal derivative-free methods for multiple roots <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>m</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> of nonlinear expressions is one of the most fascinating and difficult problems in the area of numerical analysis and Computational mathematics. In this study, we introduce a new fourth order optimal family of Ostrowski’s method without derivatives for multiple roots of nonlinear equations. Initially the convergence analysis is performed for particular values of multiple roots—afterwards it concludes in general form. Moreover, the applicability and comparison demonstrated on three real life problems (e.g., Continuous stirred tank reactor (CSTR), Plank’s radiation and Van der Waals equation of state) and two standard academic examples that contain the clustering of roots and higher-order multiplicity <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>m</mi><mo>=</mo><mn>100</mn><mo>)</mo></mrow></semantics></math></inline-formula> problems, with existing methods. Finally, we observe from the computational results that our methods consume the lowest CPU timing as compared to the existing ones. This illustrates the theoretical outcomes to a great extent of this study. |
| first_indexed | 2024-03-10T15:34:17Z |
| format | Article |
| id | doaj.art-2bcbc70543d044488066ca9bff52c694 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:34:17Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2bcbc70543d044488066ca9bff52c6942023-11-20T17:22:08ZengMDPI AGMathematics2227-73902020-10-01810180910.3390/math8101809An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear EquationsRamandeep Behl0Samaher Khalaf Alharbi1Fouad Othman Mallawi2Mehdi Salimi3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4L8, CanadaFinding higher-order optimal derivative-free methods for multiple roots <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>m</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></semantics></math></inline-formula> of nonlinear expressions is one of the most fascinating and difficult problems in the area of numerical analysis and Computational mathematics. In this study, we introduce a new fourth order optimal family of Ostrowski’s method without derivatives for multiple roots of nonlinear equations. Initially the convergence analysis is performed for particular values of multiple roots—afterwards it concludes in general form. Moreover, the applicability and comparison demonstrated on three real life problems (e.g., Continuous stirred tank reactor (CSTR), Plank’s radiation and Van der Waals equation of state) and two standard academic examples that contain the clustering of roots and higher-order multiplicity <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>m</mi><mo>=</mo><mn>100</mn><mo>)</mo></mrow></semantics></math></inline-formula> problems, with existing methods. Finally, we observe from the computational results that our methods consume the lowest CPU timing as compared to the existing ones. This illustrates the theoretical outcomes to a great extent of this study.https://www.mdpi.com/2227-7390/8/10/1809nonlinear equationKing–Traub conjecturemultiple rootoptimal iterative methodefficiency index |
| spellingShingle | Ramandeep Behl Samaher Khalaf Alharbi Fouad Othman Mallawi Mehdi Salimi An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations Mathematics nonlinear equation King–Traub conjecture multiple root optimal iterative method efficiency index |
| title | An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations |
| title_full | An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations |
| title_fullStr | An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations |
| title_full_unstemmed | An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations |
| title_short | An Optimal Derivative-Free Ostrowski’s Scheme for Multiple Roots of Nonlinear Equations |
| title_sort | optimal derivative free ostrowski s scheme for multiple roots of nonlinear equations |
| topic | nonlinear equation King–Traub conjecture multiple root optimal iterative method efficiency index |
| url | https://www.mdpi.com/2227-7390/8/10/1809 |
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