- -

A new fourth-order family for solving nonlinear problems and its dynamics

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

A new fourth-order family for solving nonlinear problems and its dynamics

Mostrar el registro completo del ítem

Cordero Barbero, A.; Feng, L.; Magrenan, A.; Torregrosa Sánchez, JR. (2015). A new fourth-order family for solving nonlinear problems and its dynamics. Journal of Mathematical Chemistry. 53(3):893-910. https://doi.org/10.1007/s10910-014-0464-4

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/66348

Ficheros en el ítem

Thumbnail
Nombre: CTFamily.pdf
Tamaño: 983.2Kb
Formato: PDF
Descripción: Versión del Autor.
Abrir/Preview
[Cerrado]
Nombre: -Cordero;Torregro ...
Tamaño: 1.381Mb
Formato: PDF
Descripción: Versión editorial
Solicitar una copia al autor

Metadatos del ítem

Título: A new fourth-order family for solving nonlinear problems and its dynamics
Autor: Cordero Barbero, Alicia Feng, Licheng Magrenan, A. Torregrosa Sánchez, Juan Ramón
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...[+]
Palabras clave: Nonlinear systems , Iterative methods , Complex dynamics , Parameter space , Basins of attraction , Stability
Derechos de uso: Reserva de todos los derechos
Fuente:
Journal of Mathematical Chemistry. (issn: 0259-9791 )
DOI: 10.1007/s10910-014-0464-4
Editorial:
Springer Verlag (Germany)
Versión del editor: http://dx.doi.org/10.1007/s10910-014-0464-4
Título del congreso: 14th International Conference of Computational and Mathematical Methods in Science and Engineering (CMMSE)
Lugar del congreso: Rota, Spain
Fecha congreso: JUL 03-07, 2014
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/
info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-01/ES/PROCESOS ITERATIVOS PARA RESOLVER ECUACIONES NO LINEALES: CONSTRUCCION, CONVERGENCIA, EFICIENCIA, ANALISIS DINAMICO Y APLICACIONES/
info:eu-repo/grantAgreement/UPV//SP20120474/
Agradecimientos:
This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-{01, 02} and Universitat Politecnica de Valencia SP20120474.
Tipo: Artículo Comunicación en congreso

References

R.C. Rach, J.S. Duan, A.M. Wazwaz, Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. J. Math. Chem. 52(1), 255–267 (2014)

R. Singh, G. Nelakanti, J. Kumar, A new efficient technique for solving two-point boundary value problems for integro-differential equations. J. Math. Chem. doi: 10.1007/s10910-014-0363-8

M. Mahalakshmi, G. Hariharan, K. Kannan, The wavelet methods to linear and nonlineal reaction–diffusion model arising in mathematical chemistry. J. Math. Chem. 51, 2361–2385 (2013) [+]
R.C. Rach, J.S. Duan, A.M. Wazwaz, Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the Adomian decomposition method. J. Math. Chem. 52(1), 255–267 (2014)

R. Singh, G. Nelakanti, J. Kumar, A new efficient technique for solving two-point boundary value problems for integro-differential equations. J. Math. Chem. doi: 10.1007/s10910-014-0363-8

M. Mahalakshmi, G. Hariharan, K. Kannan, The wavelet methods to linear and nonlineal reaction–diffusion model arising in mathematical chemistry. J. Math. Chem. 51, 2361–2385 (2013)

P.G. Logrado, J.D.M. Vianna, Partitioning technique procedure revisited: formalism and first application to atomic problems. J. Math. Chem. 22, 107–116 (1997)

C.G. Jesudason, I. Numerical nonlinear analysis: differential methods and optimization applied to chemical reaction rate determination. J. Math. Chem. 49, 1384–1415 (2011)

A. Klamt, Conductor-like screening model for real solvents: a new approach to the quantitative calculation of solvation phenomena. J. Phys. Chem. 99, 2224–2235 (1995)

A. Klamt, V. Jonas, T. Brger, J.C.W. Lohrenz, Refinement and parametrization of COSMORS. J. Phys. Chem. A 102, 5074–5085 (1998)

H. Grensemann, J. Gmehling, Performance of a conductor-like screening model for real solvents model in comparison to classical group contribution methods. Ind. Eng. Chem. Res. 44(5), 1610–1624 (2005)

T. Banerjee, A. Khanna, Infinite dilution activity coefficients for trihexyltetradecyl phosphonium ionic liquids: measurements and COSMO-RS prediction. J. Chem. Eng. Data 51(6), 2170–2177 (2006)

R. Franke, B. Hannebauer, On the influence of basis sets and quantum chemical methods on the prediction accuracy of COSMO-RS. Phys. Chem. Chem. Phys. 13, 21344–21350 (2011)

K. Maleknejad, M. Alizadeh, An efficient numerical scheme for solving Hammerstein integral equation arisen in chemical phenomenon. Proc. Comput. Sci. 3, 361–364 (2011)

M. Petković, B. Neta, L. Petković, J. Džunić, Multipoint Methods for Solving Nonlinear Equations (Academic Press, Amsterdam, 2012)

A. Cordero, J.R. Torregrosa, Variants of Newton’s method using fifth-order quadrature formulas. Appl. Math. Comput. 190, 686–698 (2007)

H.T. Kung, J.F. Traub, Optimal order of one-point and multi-point iterations. J. Assoc. Comput. Math. 21, 643–651 (1974)

A.M. Ostrowski, Solution of Equations and Systems of Equations (Prentice-Hall, Englewood Cliffs, 1964)

P. Jarratt, Some fourth order multipoint iterative methods for solving equations. Math. Comput. 20, 434–437 (1966)

R.F. King, A family of fourth order methods for nonlinear equations. SIAM J. Numer. Anal. 10, 876–879 (1973)

A. Cordero, J.L. Hueso, E. Martínez, J.R. Torregrosa, A modified Newton Jarratt’s composition. Numer. Algorithms 55, 87–99 (2010)

S. Amat, S. Busquier, Á.A. Magreñán, Reducing Chaos and Bifurcations in Newton-Type Methods. Abstract and Applied Analysis Volume 2013 (2013), Article ID 726701, 10 pages, doi: 10.1155/2013/726701

S. Amat, S. Busquier, S. Plaza, Review of some iterative root-finding methods from a dynamical point of view. Sci. Ser. A Math. Sci. 10, 3–35 (2004)

F. Chicharro, A. Cordero, J.M. Gutiérrez, J.R. Torregrosa, Complex dynamics of derivative-free methods for nonlinear equations. Appl. Math. Comput. 219, 7023–7035 (2013)

C. Chun, M.Y. Lee, B. Neta, J. Džunić, On optimal fourth-order iterative methods free from second derivative and their dynamics. Appl. Math. Comput. 218, 6427–6438 (2012)

Á.A. Magreñán, Different anomalies in a Jarratt family of iterative root-finding methods. Appl. Math. Comput. 233, 29–38 (2014)

A. Cordero, J.R. Torregrosa, P. Vindel, Dynamics of a family of Chebyshev–Halley type methods. Appl. Math. Comput. 219, 8568–8583 (2013)

Á. A. Magreñán, Estudio de la dinámica del método de Newton amortiguado (PhD Thesis). Servicio de Publicaciones, Universidad de La Rioja, (2013). http://dialnet.unirioja.es/servlet/tesis?codigo=38821

P. Blanchard, The dynamics of Newton’s method. Proc. Symp. Appl. Math. 49, 139–154 (1994)

F. Chicharro, A. Cordero, J.R. Torregrosa, Drawing dynamical and parameters planes of iterative families and methods. The Scientific World J. 2013 (Article ID 780153) (2013)

L.B. Rall, Computational Solution of Nonlinear Operator Equations (Robert E. Krieger Publishing Company Inc., New York, 1969)

J.R. Sharma, R.K. Guna, R. Sharma, An efficient fourth order weighted-Newton method for systems of nonlinear equations. Numer. Algorithms 62, 307–323 (2013)

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem