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A Renormalization Group Method for Nonlinear Oscillators
Author(s) -
Mudavanhu B.,
O'Malley, Jr. R. E.
Publication year - 2001
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.1071178
Subject(s) - renormalization group , mathematics , nonlinear system , renormalization , method of averaging , group (periodic table) , order (exchange) , mathematical physics , mathematical analysis , asymptotic expansion , statistical physics , physics , quantum mechanics , finance , economics
We present a new approach for finding the asymptotic solution of certain weakly nonlinear oscillator equations. In particular, we develop a simplified version of the renormalization group method of Chen, et al. to obtain higher‐order approximations on longer time intervals than are typically provided by averaging and two‐timing. The technique, which has much greater potential, is illustrated on three challenging examples from the literature for which better than usual asymptotic solutions are obtained.