A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator
In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that one element of this family has order five. The proposed methods have four steps an...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/9/776 |
| _version_ | 1819037275066990592 |
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| author | Alicia Cordero Cristina Jordán Esther Sanabria Juan R. Torregrosa |
| author_facet | Alicia Cordero Cristina Jordán Esther Sanabria Juan R. Torregrosa |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that one element of this family has order five. The proposed methods have four steps and, in all of them, the same divided difference operator appears. Numerical problems, including systems of academic interest and the system resulting from the discretization of the boundary problem described by Fisher’s equation, are shown to compare the performance of the proposed schemes with other known ones. The numerical tests are in concordance with the theoretical results. |
| first_indexed | 2024-12-21T08:18:49Z |
| format | Article |
| id | doaj.art-3eb50c13486e47538113c9c809a7c390 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T08:18:49Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-3eb50c13486e47538113c9c809a7c3902022-12-21T19:10:29ZengMDPI AGMathematics2227-73902019-08-017977610.3390/math7090776math7090776A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences OperatorAlicia Cordero0Cristina Jordán1Esther Sanabria2Juan R. Torregrosa3Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, SpainMultidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, SpainDepartment of Applied Mathematics, Universitat Politènica de València, 46022 València, SpainMultidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, SpainIn this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that one element of this family has order five. The proposed methods have four steps and, in all of them, the same divided difference operator appears. Numerical problems, including systems of academic interest and the system resulting from the discretization of the boundary problem described by Fisher’s equation, are shown to compare the performance of the proposed schemes with other known ones. The numerical tests are in concordance with the theoretical results.https://www.mdpi.com/2227-7390/7/9/776nonlinear systemsmultipoint iterative methodsdivided difference operatororder of convergenceNewton’s methodcomputational efficiency index |
| spellingShingle | Alicia Cordero Cristina Jordán Esther Sanabria Juan R. Torregrosa A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator Mathematics nonlinear systems multipoint iterative methods divided difference operator order of convergence Newton’s method computational efficiency index |
| title | A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator |
| title_full | A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator |
| title_fullStr | A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator |
| title_full_unstemmed | A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator |
| title_short | A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator |
| title_sort | new class of iterative processes for solving nonlinear systems by using one divided differences operator |
| topic | nonlinear systems multipoint iterative methods divided difference operator order of convergence Newton’s method computational efficiency index |
| url | https://www.mdpi.com/2227-7390/7/9/776 |
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