International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1984 / Article

Open Access

Volume 7 |Article ID 321902 | https://doi.org/10.1155/S0161171284000156

L. E. Levine, W. C. Obi, "Generalized multitime expansions for equations with slowly varying coefficients", International Journal of Mathematics and Mathematical Sciences, vol. 7, Article ID 321902, 8 pages, 1984. https://doi.org/10.1155/S0161171284000156

Generalized multitime expansions for equations with slowly varying coefficients

Received18 Apr 1983

Abstract

The successive terms in a uniformly valid multitime expansion of the solutions of constant coefficient differential equations containing a small parameter ϵ may be obtained without resorting to secularity conditions if the time scales ti=ϵit(i=0,1,) are used. Similar results have been achieved in some cases for equations with variable coefficients by using nonlinear time scales generated from the equations themselves. This paper extends the latter approach to the general second order ordinary differential equation with slowly varying coefficients and examines the restrictions imposed by the method.

Copyright © 1984 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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