Construction of An Approximate Periodic Solution to a Modified Lewis Equation

Details Construction of An Approximate Periodic Solution to a Modified Lewis Equation Construction of An Approximate Periodic Solution to a Modified Lewis Equation

Mar 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aps..aprt14007o&link_type=abstract

American Physical Society, APS April Meeting 2012, March 31-Apr 3, 2012, abstract #T14.007

Physics

Scientific paper

There have been many papers published on the construction of approximate periodic solutions of various types of non-linear differential equations. Many techniques have also been developed for obtaining approximate solutions. Among them are the method of Krylov-Bogoliubov-Mitropolsky, the harmonic balance, and the averaging method. We investigate the periodic solution of a modified Lewis equation "x+x^3=?(1-|x|)'x, * where ? is a small and positive parameter, because of its strong cubic nonlinearity. Using an extension of the Mickens-Oyedeji method [1] developed by Cveticanin [2], we calculate the exact angular frequency for the equation "x+x^3=0, ** and using the result of a first-order averaging method to calculate the approximate periodic solution of Eq. (*). Our result is compared with numerical calculations and there is a good agreement between our result and numerical calculations.

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