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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 263467, 8 pages
http://dx.doi.org/10.1155/2013/263467
Research Article

A New Extended Padé Approximation and Its Application

1Department of Mathematics, Birjand University, Birjand, Iran
2Faculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran

Received 19 June 2013; Revised 16 September 2013; Accepted 7 October 2013

Academic Editor: Weimin Han

Copyright © 2013 Z. Kalateh Bojdi 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. G. A. Baker and P. Graves-Morris, Padé Approximants, Addison-Wesley, 1981.
  2. G. A. Baker, Essentials of Padé Approximants, Academic Press, New York, NY, USA, 1975.
  3. A. Cuyt, “Multivariate Padé approximants revisited,” BIT, vol. 26, no. 1, pp. 71–79, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Wuytack, “On the osculatory rational interpolation problem,” Mathematics and Computers in Simulation, vol. 29, pp. 837–843, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. A. M. Cuyt and B. M. Verdonk, “General order Newton-Padé approximants for multivariate functions,” Numerische Mathematik, vol. 43, no. 2, pp. 293–307, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. Borwein and T. Erdélyi, Polynomials and Polynomials Inequalities, vol. 161 of Graduate Texts in Mathematics, Springer, Berlin, Germany, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Z. M. Odibat and N. T. Shawagfeh, “Generalized Taylor's formula,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 286–293, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  9. D. Funaro, Polynomial Approximations of Differential Equations, Springer, 1992. View at MathSciNet
  10. J. S. Hesthaven, S. Gottlieb, and D. Gottlieb, Spectral Methods for Time-Dependent Problems, Cambridge University, 2009.
  11. P. Mokhtary and F. Ghoreishi, “The L2-convergence of the Legendre spectral tau matrix formulation for nonlinear fractional integro differential equations,” Numerical Algorithms, vol. 58, no. 4, pp. 475–496, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  12. I. V. Andrianov and J. Awrejcewicz, “Analysis of jump phenomena using Padé approximations,” Journal of Sound and Vibration, vol. 260, no. 3, pp. 577–588, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. I. Andrianov and J. Awrejcewicz, “Solutions in the Fourier series form, Gibbs phenomena and Padé approximants,” Journal of Sound and Vibration, vol. 245, no. 4, pp. 753–756, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. I. V. Andrianov and J. Awrejcewicz, “Iterative determination of homoclinic orbit parameters and Padé approximants,” Journal of Sound and Vibration, vol. 240, no. 2, pp. 394–397, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. G. Kudra and J. Awrejcewicz, “Tangents hyperbolic approximations of the spatial model of friction coupled with rolling resistance,” International Journal of Bifurcation and Chaos, vol. 21, pp. 2905–2917, 2011.
  16. O. D. Makinde, “Solving microwave heating model in a slab using Hermite-Padé approximation technique,” Applied Thermal Engineering, vol. 27, pp. 599–603, 2007.