Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Exponential asymptotic expansions for nonlinear differential equations

Author: William B. Day
Journal: Quart. Appl. Math. 37 (1979), 169-176
MSC: Primary 34E05; Secondary 34A34
DOI: https://doi.org/10.1090/qam/542989
MathSciNet review: 542989
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Abstract: An exponential method for obtaining asymptotic expansions of the solution of a linear differential equation was presented by Brull and Soler in [3], We extend this method to the nonlinear differential equation of the type $ L\left( u \right) + {\Sigma _1}^Nf\left( {x, t} \right){u^n} = 0$, where $ t$ is the small parameter. Three examples are used to illustrate the technique and to explain how uniformly valid expansions may be obtained.

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DOI: https://doi.org/10.1090/qam/542989
Article copyright: © Copyright 1979 American Mathematical Society

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