Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On perturbation methods involving expansions in terms of a parameter

Author: Richard Bellman
Journal: Quart. Appl. Math. 13 (1955), 195-200
MSC: Primary 34.0X
DOI: https://doi.org/10.1090/qam/70792
MathSciNet review: 70792
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Abstract: It is shown by means of some examples from the theories of linear algebraic equations, linear integral equations and nonlinear differential equations that the effectiveness of the method of expanding a solution in a power series in terms of a parameter may in many cases be greatly increased by expanding in terms of a suitably chosen function of the parameter. This is particularly the case when the physical setting of the problem allows only positive values of the parameter to enter.

References [Enhancements On Off] (What's this?)

  • [1] Richard Bellman, A note on the summability of formal solutions of linear integral equations, Duke Math. J. 17 (1950), 53–55. MR 0032916
  • [2] Solomon Lefschetz, Lectures on Differential Equations, Annals of Mathematics Studies, no.14, Princeton Univeristy Press, Princeton, N. J.; Oxford University Press, London, 1946. MR 0016788
  • [3] M. J. Lighthill, A technique for rendering approximate solutions to physical problems uniformly valid, Philos. Mag. (7) 40 (1949), 1179–1201. MR 0033941
  • [4] J. Shohat, On van der Pol’s and non-linear differential equations, J. Appl. Phys. 15 (1944), 568–574. MR 0010322
  • [5] J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932

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DOI: https://doi.org/10.1090/qam/70792
Article copyright: © Copyright 1955 American Mathematical Society

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