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On a novel fourth-order algorithm for solving systems of nonlinear equations

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On a novel fourth-order algorithm for solving systems of nonlinear equations

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Babajee, DKR.; Cordero Barbero, A.; Soleymani, F.; Torregrosa Sánchez, JR. (2012). On a novel fourth-order algorithm for solving systems of nonlinear equations. Journal of Applied Mathematics. 2012. https://doi.org/10.1155/2012/165452

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Título: On a novel fourth-order algorithm for solving systems of nonlinear equations
Autor: Babajee, Diyashvir K. R. Cordero Barbero, Alicia Soleymani, Fazlollah Torregrosa Sánchez, Juan Ramón
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
This paper focuses on solving systems of nonlinear equations numerically. We propose an efficient iterative scheme including two steps and fourth order of convergence. The proposed method does not require the evaluation ...[+]
Palabras clave: Quadrature-formulas
Derechos de uso: Reconocimiento (by)
Fuente:
Journal of Applied Mathematics. (issn: 1110-757X ) (eissn: 1687-0042 )
DOI: 10.1155/2012/165452
Editorial:
Hindawi Publishing Corporation
Versión del editor: http://dx.doi.org/10.1155/2012/165452
Código del Proyecto:
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
Agradecimientos:
The authors would like to thank the referees for the valuable comments and for the suggestions to improve the readability of the paper. This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02.[+]
Tipo: Artículo

References

Babajee, D. K. R., Dauhoo, M. Z., Darvishi, M. T., Karami, A., & Barati, A. (2010). Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations. Journal of Computational and Applied Mathematics, 233(8), 2002-2012. doi:10.1016/j.cam.2009.09.035

Darvishi, M. T., & Barati, A. (2007). A fourth-order method from quadrature formulae to solve systems of nonlinear equations. Applied Mathematics and Computation, 188(1), 257-261. doi:10.1016/j.amc.2006.09.115

Soleymani, F., Khattri, S. K., & Karimi Vanani, S. (2012). Two new classes of optimal Jarratt-type fourth-order methods. Applied Mathematics Letters, 25(5), 847-853. doi:10.1016/j.aml.2011.10.030 [+]
Babajee, D. K. R., Dauhoo, M. Z., Darvishi, M. T., Karami, A., & Barati, A. (2010). Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations. Journal of Computational and Applied Mathematics, 233(8), 2002-2012. doi:10.1016/j.cam.2009.09.035

Darvishi, M. T., & Barati, A. (2007). A fourth-order method from quadrature formulae to solve systems of nonlinear equations. Applied Mathematics and Computation, 188(1), 257-261. doi:10.1016/j.amc.2006.09.115

Soleymani, F., Khattri, S. K., & Karimi Vanani, S. (2012). Two new classes of optimal Jarratt-type fourth-order methods. Applied Mathematics Letters, 25(5), 847-853. doi:10.1016/j.aml.2011.10.030

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2010). Accelerated methods of order <mml:math altimg=«si12.gif» display=«inline» overflow=«scroll» xmlns:xocs=«http://www.elsevier.com/xml/xocs/dtd» xmlns:xs=«http://www.w3.org/2001/XMLSchema» xmlns:xsi=«http://www.w3.org/2001/XMLSchema-instance» xmlns=«http://www.elsevier.com/xml/ja/dtd» xmlns:ja=«http://www.elsevier.com/xml/ja/dtd» xmlns:mml=«http://www.w3.org/1998/Math/MathML» xmlns:tb=«http://www.elsevier.com/xml/common/table/dtd» xmlns:sb=«http://www.elsevier.com/xml/common/struct-bib/dtd» xmlns:ce=«http://www.elsevier.com/xml/common/dtd» xmlns:xlink=«http://www.w3.org/1999/xlink» xmlns:cals=«http://www.elsevier.com/xml/common/cals/dtd»><mml:mn>2</mml:mn><mml:mi>p</mml:mi></mml:math> for systems of nonlinear equations. Journal of Computational and Applied Mathematics, 233(10), 2696-2702. doi:10.1016/j.cam.2009.11.018

Dayton, B. H., Li, T.-Y., & Zeng, Z. (2011). Multiple zeros of nonlinear systems. Mathematics of Computation, 80(276), 2143-2143. doi:10.1090/s0025-5718-2011-02462-2

Haijun, W. (2008). New third-order method for solving systems of nonlinear equations. Numerical Algorithms, 50(3), 271-282. doi:10.1007/s11075-008-9227-2

Noor, M. A., Waseem, M., Noor, K. I., & Al-Said, E. (2012). Variational iteration technique for solving a system of nonlinear equations. Optimization Letters, 7(5), 991-1007. doi:10.1007/s11590-012-0479-3

Frontini, M., & Sormani, E. (2004). Third-order methods from quadrature formulae for solving systems of nonlinear equations. Applied Mathematics and Computation, 149(3), 771-782. doi:10.1016/s0096-3003(03)00178-4

Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). A modified Newton-Jarratt’s composition. Numerical Algorithms, 55(1), 87-99. doi:10.1007/s11075-009-9359-z

Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062

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