New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns
In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/6/12/296 |
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| author | Ramandeep Behl Alicia Cordero Juan R. Torregrosa Ali Saleh Alshomrani |
| author_facet | Ramandeep Behl Alicia Cordero Juan R. Torregrosa Ali Saleh Alshomrani |
| author_sort | Ramandeep Behl |
| collection | DOAJ |
| description | In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature. |
| first_indexed | 2024-12-10T15:21:14Z |
| format | Article |
| id | doaj.art-2260c8a8abaf427885fc428812ef8925 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-10T15:21:14Z |
| publishDate | 2018-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2260c8a8abaf427885fc428812ef89252022-12-22T01:43:41ZengMDPI AGMathematics2227-73902018-12-0161229610.3390/math6120296math6120296New Iterative Methods for Solving Nonlinear Problems with One and Several UnknownsRamandeep Behl0Alicia Cordero1Juan R. Torregrosa2Ali Saleh Alshomrani3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaMultidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, SpainMultidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 Valencia, SpainDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaIn this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, with the flexibility through weight function/s or free parameter/s at both substeps, as well as small residual errors and asymptotic error constants. In addition, we generalize these schemes to nonlinear systems preserving the order of convergence. Regarding the applicability of the proposed techniques, we choose some real-world problems, namely chemical fractional conversion and the trajectory of an electron in the air gap between two parallel plates, in order to study the multi-factor effect, fractional conversion of species in a chemical reactor, Hammerstein integral equation, and a boundary value problem. Moreover, we find that our proposed schemes run better than or equal to the existing ones in the literature.https://www.mdpi.com/2227-7390/6/12/296nonlinear equationslocal convergence analysisorder of convergenceNewton’s methodmulti-point iterative methodscomputational order of convergence |
| spellingShingle | Ramandeep Behl Alicia Cordero Juan R. Torregrosa Ali Saleh Alshomrani New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns Mathematics nonlinear equations local convergence analysis order of convergence Newton’s method multi-point iterative methods computational order of convergence |
| title | New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns |
| title_full | New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns |
| title_fullStr | New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns |
| title_full_unstemmed | New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns |
| title_short | New Iterative Methods for Solving Nonlinear Problems with One and Several Unknowns |
| title_sort | new iterative methods for solving nonlinear problems with one and several unknowns |
| topic | nonlinear equations local convergence analysis order of convergence Newton’s method multi-point iterative methods computational order of convergence |
| url | https://www.mdpi.com/2227-7390/6/12/296 |
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