International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 151-158

Generalized multitime expansions for equations with slowly varying coefficients

L. E. Levine and W. C. Obi

Department of Pure and Applied Mathematics, Stevens Institute of Technology, Hoboken 07030, New Jersey, USA

Received 18 April 1983

Copyright © 1984 L. E. Levine and W. C. Obi. 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.


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.