A General Optimal Iterative Scheme with Arbitrary Order of Convergence
A general optimal iterative method, for approximating the solution of nonlinear equations, of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>n<...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/884 |
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| author | Alicia Cordero Juan R. Torregrosa Paula Triguero-Navarro |
| author_facet | Alicia Cordero Juan R. Torregrosa Paula Triguero-Navarro |
| author_sort | Alicia Cordero |
| collection | DOAJ |
| description | A general optimal iterative method, for approximating the solution of nonlinear equations, of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> steps with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> order of convergence is presented. Cases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> correspond to Newton’s and Ostrowski’s schemes, respectively. The basins of attraction of the proposed schemes on different test functions are analyzed and compared with the corresponding to other known methods. The dynamical planes showing the different symmetries of the basins of attraction of new and known methods are presented. The performance of different methods on some test functions is shown. |
| first_indexed | 2024-03-10T11:21:40Z |
| format | Article |
| id | doaj.art-1dba5d1cb93045c9a0bc973268376518 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:21:40Z |
| publishDate | 2021-05-01 |
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| series | Symmetry |
| spelling | doaj.art-1dba5d1cb93045c9a0bc9732683765182023-11-21T19:58:54ZengMDPI AGSymmetry2073-89942021-05-0113588410.3390/sym13050884A General Optimal Iterative Scheme with Arbitrary Order of ConvergenceAlicia Cordero0Juan R. Torregrosa1Paula Triguero-Navarro2Multidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, SpainMultidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, SpainMultidisciplinary Institute of Mathematics, Universitat Politènica de València, 46022 València, SpainA general optimal iterative method, for approximating the solution of nonlinear equations, of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> steps with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></semantics></math></inline-formula> order of convergence is presented. Cases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> correspond to Newton’s and Ostrowski’s schemes, respectively. The basins of attraction of the proposed schemes on different test functions are analyzed and compared with the corresponding to other known methods. The dynamical planes showing the different symmetries of the basins of attraction of new and known methods are presented. The performance of different methods on some test functions is shown.https://www.mdpi.com/2073-8994/13/5/884nonlinear equationiterative methodconvergencebasin of attractionstability |
| spellingShingle | Alicia Cordero Juan R. Torregrosa Paula Triguero-Navarro A General Optimal Iterative Scheme with Arbitrary Order of Convergence Symmetry nonlinear equation iterative method convergence basin of attraction stability |
| title | A General Optimal Iterative Scheme with Arbitrary Order of Convergence |
| title_full | A General Optimal Iterative Scheme with Arbitrary Order of Convergence |
| title_fullStr | A General Optimal Iterative Scheme with Arbitrary Order of Convergence |
| title_full_unstemmed | A General Optimal Iterative Scheme with Arbitrary Order of Convergence |
| title_short | A General Optimal Iterative Scheme with Arbitrary Order of Convergence |
| title_sort | general optimal iterative scheme with arbitrary order of convergence |
| topic | nonlinear equation iterative method convergence basin of attraction stability |
| url | https://www.mdpi.com/2073-8994/13/5/884 |
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