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Numerical Applications and Padé Approximants

  • Abdul-Majid Wazwaz
Part of the Nonlinear Physical Science book series (NPS)

Abstract

In this chapter we will apply Adominan decomposition method, the variational iteration method, and other numerical methods to handle linear and nonlinear differential equations numerically. Because the decomposition method and the variational iteration method provide a rapidly convergent series and approximations and faster than existing numerical techniques, it is therefore the two methods are considered efficient, reliable and easy to use from a computational viewpoint. It is to be noted that few terms or few approximations are usually needed to supply a reliable result much closer to the exact value. The overall error can be significantly decreased by computing additional terms of the decomposition series or additional approximations.

Keywords

Taylor Series Decomposition Method Numerical Application Recursive Relation Series Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, (1994).zbMATHGoogle Scholar
  2. 2.
    W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Vol I, Academic Press, New York, (1965).Google Scholar
  3. 3.
    G.A. Baker, Essentials of Padé Approximants, Academic Press, London, (1975).zbMATHGoogle Scholar
  4. 4.
    G.A. Baker and P. Graves-Morris, Essentials of Padé Approximants, Cambridge University Press, Cambridge, (1996).CrossRefGoogle Scholar
  5. 5.
    J. Boyd, Padé approximant algorithm for solving nonlinear ordinary differential equation, boundary value problems on an unbounded domain, Computers in Physics, 11(3), 299–303, (1997).CrossRefGoogle Scholar
  6. 6.
    J.H. He, Some asymptotic methods for strongly nonlinearly equations, Internat. J. of Modern Math., 20(10), 1141–1199, (2006).zbMATHGoogle Scholar
  7. 7.
    H.K. Kuiken, On boundary layers in field mechanics that decay algebraically along stretches of wall that are not vanishing small, IMA J. Applied Math., 27, 387–405, (1981).zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A.M. Wazwaz, Analytical approximations and Padé approximants for Volterra’s population model, Appl. Math. and Comput., 100, 31–25, (1999).MathSciNetCrossRefGoogle Scholar
  9. 9.
    A.M. Wazwaz, The modified decomposition method and Padé approximants for solving Thomas-Fermi equation, Appl. Math. and Comput., 105, 11–19, (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Leiden, (2002).zbMATHGoogle Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Abdul-Majid Wazwaz
    • 1
  1. 1.Department of MathematicsSaint Xavier UniversityChicagoUSA

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