Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs

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dc.contributor	Universitat Politècnica de Catalunya. Departament d'Enginyeria Electrònica
dc.contributor	Universitat Politècnica de Catalunya. GAA - Grup d'Astronomia i Astrofísica
dc.contributor.author	Ahmad, Fayyaz
dc.contributor.author	Tohidi, Emran
dc.contributor.author	Ullah, Malik Zaka
dc.contributor.author	Carrasco, Juan A.
dc.date	2015-08-01
dc.identifier.citation	Ahmad, F., Tohidi, E., Ullah, M., Carrasco, J. Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs. "Computers & mathematics with applications", 01 Agost 2015, vol. 70, núm. 4, p. 624-636.
dc.identifier.citation	0898-1221
dc.identifier.citation	10.1016/j.camwa.2015.05.012
dc.identifier.uri	http://hdl.handle.net/2117/83353
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science/article/pii/S0898122115002357
dc.relation	info:eu-repo/grantAgreement/ES/6PN/AYA2010-15685
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Iterative methods
dc.subject	Differential equations, Nonlinear
dc.subject	Newton-Raphson method
dc.subject	Multi-step iterative methods
dc.subject	Systems of nonlinear equations
dc.subject	Newton's method
dc.subject	Computational efficiency
dc.subject	Nonlinear ordinary differential equations
dc.subject	Nonlinear partial differential equations
dc.subject	iterative methods
dc.subject	numerical-solution
dc.subject	newtons method
dc.subject	general-class
dc.subject	convergence
dc.subject	Mètodes iteratius (Matemàtica)
dc.subject	Equacions diferencials no lineals
dc.subject	Newton-Raphson, Mètode de
dc.title	Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs
dc.type	info:eu-repo/semantics/updatedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	This paper proposes a multi-step iterative method for solving systems of nonlinear equations with a local convergence order of 3m - 4, where in (>= 2) is the number of steps. The multi-step iterative method includes two parts: the base method and the multi-step part. The base method involves two function evaluations, two Jacobian evaluations, one LU decomposition of a Jacobian, and two matrix-vector multiplications. Every stage of the multi-step part involves the solution of two triangular linear systems and one matrix-vector multiplication. The computational efficiency of the new method is better than those of previously proposed methods. The method is applied to several nonlinear problems resulting from discretizing nonlinear ordinary differential equations and nonlinear partial differential equations. (C) 2015 Elsevier Ltd. All rights reserved.

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