Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs
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...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/83353 |
| Acceso en línea: | https://hdl.handle.net/2117/83353 https://dx.doi.org/10.1016/j.camwa.2015.05.012 |
| Access Level: | acceso abierto |
| Palabra clave: | Iterative methods Differential equations, Nonlinear Newton-Raphson method Multi-step iterative methods Systems of nonlinear equations Newton's method Computational efficiency Nonlinear ordinary differential equations Nonlinear partial differential equations iterative methods numerical-solution newtons method general-class convergence Mètodes iteratius (Matemàtica) Equacions diferencials no lineals Newton-Raphson, Mètode de Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | 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. |
|---|