Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
[EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some kn...
| Authors: | ; ; ; |
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| Format: | Article |
| Publication date: | 2019 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/180475 |
| Online Access: | https://riunet.upv.es/handle/10251/180475 |
| Access Level: | Open access |
| Keyword: | Nonlinear equations Potra-Pták method Optimal methods Weight function Basin of attraction Engineering applications MATEMATICA APLICADA |
| Summary: | [EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some known methods of the corresponding order. It is proved that the results obtained from the proposed methods are compatible with other methods. The proposed methods are tested on some problems related to engineering and science. Furthermore, applying these methods on quadratic and cubic polynomials, their stability is analyzed by means of their basins of attraction. |
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