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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston, (1994).
W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Vol I, Academic Press, New York, (1965).
G.A. Baker, Essentials of Padé Approximants, Academic Press, London, (1975).
G.A. Baker and P. Graves-Morris, Essentials of Padé Approximants, Cambridge University Press, Cambridge, (1996).
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).
J.H. He, Some asymptotic methods for strongly nonlinearly equations, Internat. J. of Modern Math., 20(10), 1141–1199, (2006).
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).
A.M. Wazwaz, Analytical approximations and Padé approximants for Volterra’s population model, Appl. Math. and Comput., 100, 31–25, (1999).
A.M. Wazwaz, The modified decomposition method and Padé approximants for solving Thomas-Fermi equation, Appl. Math. and Comput., 105, 11–19, (1999).
A.M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Leiden, (2002).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wazwaz, AM. (2009). Numerical Applications and Padé Approximants. In: Partial Differential Equations and Solitary Waves Theory. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00251-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-00251-9_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00250-2
Online ISBN: 978-3-642-00251-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)