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Journal of Optimization Theory and Applications

, Volume 32, Issue 4, pp 441–450 | Cite as

Variational perturbation method and power-series approximation method

  • S. M. Roberts
Contributed Papers

Abstract

The power-series approximation method for solving regular perturbation problems is reexamined to show why the method works. As another way to approach these problems, the variational perturbation technique is described. Although the assumptions on which each method is based and the mechanism of deriving their differential equations are different, the system of differential equations developed by each method is identical.

Key Words

Perturbation problems variational equations power-series approximation 

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References

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    Bellman, R.,Perturbation Techniques in Mathematics, Physics, and Engineering, Holt, Rinehart, and Winston, New York, New York, 1964.Google Scholar
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    Cole, J. D.,Perturbation Methods in Applied Mathematics, Blaisdell Publishing Company, Waltham, Massachusetts, 1968.Google Scholar
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    Nayfeh, A.,Perturbation Methods, John Wiley and Sons, New York, New York, 1973.Google Scholar
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    O'Malley, R. E.,Introduction to Singular Perturbations, Academic Press, New York, New York, 1974.Google Scholar
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    Van Dyke, M.,Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, California, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • S. M. Roberts
    • 1
  1. 1.IBMPalo Alto Scientific CenterPalo Alto

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