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Variation of Parameters and the Renormalization Group Method

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This paper presents a straightforward procedure for using Renormalization Group methods to solve a significant variety of perturbation problems, including some that result from applying a nonlinear version of variation of parameters. A regular perturbation procedure typically provides asymptotic solutions valid for bounded t values as a positive parameter ε tends to zero. One can eliminate secular terms by introducing a slowly‐varying amplitude obtained as a solution of an amplitude equation on intervals where εt is bounded. With sufficient stability hypotheses, the results may even hold for all t0. These ideas are illustrated for a number of nontrivial problems involving ordinary differential equations.
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Document Type: Research Article

Publication date: February 1, 2015

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