Memory in a New Variant of King’s Family for Solving Nonlinear Systems
In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided di...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1251 |
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| author | Munish Kansal Alicia Cordero Sonia Bhalla Juan R. Torregrosa |
| author_facet | Munish Kansal Alicia Cordero Sonia Bhalla Juan R. Torregrosa |
| author_sort | Munish Kansal |
| collection | DOAJ |
| description | In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided difference operators and to compute only one inverse of a matrix per iteration. Furthermore, we have extended the proposed scheme up to the sixth-order of convergence with two additional functional evaluations. In addition, these schemes are further extended to methods with memory. We illustrate their applicability by performing numerical experiments on a wide variety of practical problems, even big-sized. It is observed that these methods produce approximations of greater accuracy and are more efficient in practice, compared with the existing methods. |
| first_indexed | 2024-03-10T18:04:17Z |
| format | Article |
| id | doaj.art-77fa157689474bc1a89d29d35b0d2ecf |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:04:17Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-77fa157689474bc1a89d29d35b0d2ecf2023-11-20T08:38:37ZengMDPI AGMathematics2227-73902020-07-0188125110.3390/math8081251Memory in a New Variant of King’s Family for Solving Nonlinear SystemsMunish Kansal0Alicia Cordero1Sonia Bhalla2Juan R. Torregrosa3School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala 147004, IndiaInstitute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, SpainDepartment of Mathematics, Chandigarh University, Gharuan 140413, IndiaInstitute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, SpainIn the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided difference operators and to compute only one inverse of a matrix per iteration. Furthermore, we have extended the proposed scheme up to the sixth-order of convergence with two additional functional evaluations. In addition, these schemes are further extended to methods with memory. We illustrate their applicability by performing numerical experiments on a wide variety of practical problems, even big-sized. It is observed that these methods produce approximations of greater accuracy and are more efficient in practice, compared with the existing methods.https://www.mdpi.com/2227-7390/8/8/1251nonlinear systemsconvergence ordermulti-point methodsschemes with memory |
| spellingShingle | Munish Kansal Alicia Cordero Sonia Bhalla Juan R. Torregrosa Memory in a New Variant of King’s Family for Solving Nonlinear Systems Mathematics nonlinear systems convergence order multi-point methods schemes with memory |
| title | Memory in a New Variant of King’s Family for Solving Nonlinear Systems |
| title_full | Memory in a New Variant of King’s Family for Solving Nonlinear Systems |
| title_fullStr | Memory in a New Variant of King’s Family for Solving Nonlinear Systems |
| title_full_unstemmed | Memory in a New Variant of King’s Family for Solving Nonlinear Systems |
| title_short | Memory in a New Variant of King’s Family for Solving Nonlinear Systems |
| title_sort | memory in a new variant of king s family for solving nonlinear systems |
| topic | nonlinear systems convergence order multi-point methods schemes with memory |
| url | https://www.mdpi.com/2227-7390/8/8/1251 |
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