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Journal of Applied Mathematics
Volume 2012, Article ID 709843, 15 pages
http://dx.doi.org/10.1155/2012/709843
Research Article

New Predictor-Corrector Methods with High Efficiency for Solving Nonlinear Systems

1Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera S/N, 40022 Valencia, Spain
2Instituto Tecnológico de Santo Domingo (INTEC), avenida de Los Próceres, Galóa, 10602 Santo Domingo, Dominican Republic

Received 20 July 2012; Revised 27 August 2012; Accepted 1 September 2012

Academic Editor: Fazlollah Soleymani

Copyright © 2012 Alicia Cordero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Iliev and N. Kyurkchiev, Nontrivial Methods in Numerical Analysis: Selected Topics in Numerical Analysis, LAP LAMBERT Academic Publishing, Saarbrcken, Germany, 2010.
  2. D. D. Bruns and J. E. Bailey, “Nonlinear feedback control for operating a nonisothermal CSTR near an unstable steady state,” Chemical Engineering Science, vol. 32, pp. 257–264, 1977. View at Google Scholar
  3. J. A. Ezquerro, J. M. Gutiérrez, M. A. Hernández, and M. A. Salanova, “Chebyshev-like methods and quadratic equations,” Revue d'Analyse Numérique et de Théorie de l'Approximation, vol. 28, no. 1, pp. 23–35, 1999. View at Google Scholar
  4. Y. Zhang and P. Huang, “High-precision Time-interval Measurement Techniques and Methods,” Progress in Astronomy, vol. 24, no. 1, pp. 1–15, 2006. View at Google Scholar
  5. Y. He and C. Ding, “Using accurate arithmetics to improve numerical reproducibility and stability in parallel applications,” Journal of Supercomputing, vol. 18, pp. 259–277, 2001. View at Google Scholar
  6. N. Revol and F. Rouillier, “Motivations for an arbitrary precision interval arithmetic and the MPFI library,” Reliable Computing, vol. 11, no. 4, pp. 275–290, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “A modified Newton-Jarratt's composition,” Numerical Algorithms, vol. 55, no. 1, pp. 87–99, 2010. View at Publisher · View at Google Scholar
  8. M. Nikkhah-Bahrami and R. Oftadeh, “An effective iterative method for computing real and complex roots of systems of nonlinear equations,” Applied Mathematics and Computation, vol. 215, no. 5, pp. 1813–1820, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. B.-C. Shin, M. T. Darvishi, and C.-H. Kim, “A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3190–3198, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “Efficient high-order methods based on golden ratio for nonlinear systems,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4548–4556, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. A. Iliev and I. Iliev, “Numerical method with order t for solving system nonlinear equations,” Collection of scientific works “30 years FMI” Plovdiv 0304.11.2000, 105112, 2000.
  12. N. Kyurkchiev and A. Iliev, “A general approach to methods with a sparse Jacobian for solving nonlinear systems of equations,” Serdica Mathematical Journal, vol. 33, no. 4, pp. 433–448, 2007. View at Google Scholar
  13. B. H. Dayton, T.-Y. Li, and Z. Zeng, “Multiple zeros of nonlinear systems,” Mathematics of Computation, vol. 80, no. 276, pp. 2143–2168, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. Cordero, J. R. Torregrosa, and M. P. Vassileva, “Pseudocomposition: a technique to design predictor–corrector methods for systems of nonlinear equations,” Applied Mathematics and Computation, vol. 218, no. 23, pp. 11496–11504, 2012. View at Publisher · View at Google Scholar
  15. A. M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, NY, USA, 1966.
  16. A. Cordero and J. R. Torregrosa, “On interpolation variants of Newton's method for functions of several variables,” Journal of Computational and Applied Mathematics, vol. 234, no. 1, pp. 34–43, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. A. Cordero and J. R. Torregrosa, “Variants of Newton's method using fifth-order quadrature formulas,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 686–698, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH