Design and multidimensional extension of iterative methods for solving nonlinear problems

[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ derivative and by using a divided difference operator we construct an iterative sche...

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Detalhes bibliográficos
Autores: Artidiello, S., Vassileva, M. P., Cordero Barbero, Alicia|||0000-0002-7462-9173, Torregrosa Sánchez, Juan Ramón|||0000-0002-9893-0761
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/103797
Acesso em linha:https://riunet.upv.es/handle/10251/103797
Access Level:acceso abierto
Palavra-chave:Nonlinear systems
Iterative method
Convergence
Efficiency index
Bratu s problem
MATEMATICA APLICADA
Descrição
Resumo:[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ derivative and by using a divided difference operator we construct an iterative scheme of order six for solving nonlinear systems. The computational efficiency of the new method is compared with some known ones, obtaining good conclusions. Numerical comparisons are made with other existing methods, on standard nonlinear systems and the classical 1D-Bratu problem by transforming it in a nonlinear system by using finite differences. From this numerical examples, we confirm the theoretical results and show the performance of the presented scheme.