A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics
A geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton’s method and the convergence order of the new method is 1+2≈2.4142. The numerical examples...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Modelling and Simulation in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2015/502854 |
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| _version_ | 1832565357717487616 |
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| author | Gustavo Fernández-Torres |
| author_facet | Gustavo Fernández-Torres |
| author_sort | Gustavo Fernández-Torres |
| collection | DOAJ |
| description | A geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton’s method and the convergence order of the new method is 1+2≈2.4142. The numerical examples and the dynamical analysis show that the new method is robust and converges to the root in many cases where Newton’s method and other recently published methods fail. |
| format | Article |
| id | doaj-art-21aaa7f7f5844a38a9881eb1f2b1e667 |
| institution | Kabale University |
| issn | 1687-5591 1687-5605 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Modelling and Simulation in Engineering |
| spelling | doaj-art-21aaa7f7f5844a38a9881eb1f2b1e6672025-02-03T01:07:50ZengWileyModelling and Simulation in Engineering1687-55911687-56052015-01-01201510.1155/2015/502854502854A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its DynamicsGustavo Fernández-Torres0Departamento de Ingenieria Civil, Facultad de Estudios Superiores (FES) Aragón, Universidad Nacional Autónoma de México (UNAM), Avenida Rancho Seco s/n, 57130 Nezahualcóyotl, MEX, MexicoA geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton’s method and the convergence order of the new method is 1+2≈2.4142. The numerical examples and the dynamical analysis show that the new method is robust and converges to the root in many cases where Newton’s method and other recently published methods fail.http://dx.doi.org/10.1155/2015/502854 |
| spellingShingle | Gustavo Fernández-Torres A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics Modelling and Simulation in Engineering |
| title | A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics |
| title_full | A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics |
| title_fullStr | A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics |
| title_full_unstemmed | A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics |
| title_short | A Novel Geometric Modification to the Newton-Secant Method to Achieve Convergence of Order 1+2 and Its Dynamics |
| title_sort | novel geometric modification to the newton secant method to achieve convergence of order 1 2 and its dynamics |
| url | http://dx.doi.org/10.1155/2015/502854 |
| work_keys_str_mv | AT gustavofernandeztorres anovelgeometricmodificationtothenewtonsecantmethodtoachieveconvergenceoforder12anditsdynamics AT gustavofernandeztorres novelgeometricmodificationtothenewtonsecantmethodtoachieveconvergenceoforder12anditsdynamics |