On perturbation methods involving expansions in terms of a parameter

Bellman, Richard

doi:10.1090/qam/70792

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.

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