Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions
The construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order techniques. Our schemes are free from derivatives and have been designed to find multi...
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1530 |
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| author | Himani Arora Alicia Cordero Juan R. Torregrosa Ramandeep Behl Sattam Alharbi |
| author_facet | Himani Arora Alicia Cordero Juan R. Torregrosa Ramandeep Behl Sattam Alharbi |
| author_sort | Himani Arora |
| collection | DOAJ |
| description | The construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order techniques. Our schemes are free from derivatives and have been designed to find multiple roots (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>). The new techniques involve the weight function approach. The convergence analysis for the new family is presented in the main theorem. In addition, some special cases of the new class are discussed. We also illustrate the applicability of our methods on van der Waals, Planck’s radiation, root clustering, and eigenvalue problems. We also contrast them with the known methods. Finally, the dynamical study of iterative schemes also provides a good overview of their stability. |
| first_indexed | 2024-03-10T03:55:24Z |
| format | Article |
| id | doaj.art-3581081acad14adfa802479410e86d02 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:55:24Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-3581081acad14adfa802479410e86d022023-11-23T08:45:42ZengMDPI AGMathematics2227-73902022-05-01109153010.3390/math10091530Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear FunctionsHimani Arora0Alicia Cordero1Juan R. Torregrosa2Ramandeep Behl3Sattam Alharbi4Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, IndiaInstitute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainInstitute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, SpainDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order techniques. Our schemes are free from derivatives and have been designed to find multiple roots (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>). The new techniques involve the weight function approach. The convergence analysis for the new family is presented in the main theorem. In addition, some special cases of the new class are discussed. We also illustrate the applicability of our methods on van der Waals, Planck’s radiation, root clustering, and eigenvalue problems. We also contrast them with the known methods. Finally, the dynamical study of iterative schemes also provides a good overview of their stability.https://www.mdpi.com/2227-7390/10/9/1530nonlinear equationsSteffensen’s methodmultiple roots |
| spellingShingle | Himani Arora Alicia Cordero Juan R. Torregrosa Ramandeep Behl Sattam Alharbi Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions Mathematics nonlinear equations Steffensen’s method multiple roots |
| title | Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions |
| title_full | Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions |
| title_fullStr | Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions |
| title_full_unstemmed | Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions |
| title_short | Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions |
| title_sort | derivative free iterative schemes for multiple roots of nonlinear functions |
| topic | nonlinear equations Steffensen’s method multiple roots |
| url | https://www.mdpi.com/2227-7390/10/9/1530 |
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