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] R. Bellman, On the summability of solutions of linear integral equations, Duke Math. J. 17, 53-5 (1950) MR 0032916
  • [2] S. Lefschetz, Lectures on differential equations, Princeton University Press, 1946 MR 0016788
  • [3] J. Lighthill, A technique for rendering approximate solutions to physical problems uniformly valid, Phil. Mag. 40, 1179-1201 (1949) MR 0033941
  • [4] J. Shohat, On Van der Pol's and related nonlinear differential equations, J. Appl. Physics 15, 568-574 (1944) MR 0010322
  • [5] J. J. Stoker, Nonlinear vibrations, Interscience, New York, 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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