Improved Lindstedt-Poincare method for the solution of nonlinear problems

Details Improved Lindstedt-Poincare method for the solution of nonlinear problems Improved Lindstedt-Poincare method for the solution of nonlinear problems

2003-03-23

arxiv.org/abs/math-ph/0303052v1

Journal of Sound and Vibrations 283, 1111-1132 (2005)

Physics

Mathematical Physics

24 pages, 7 figures, RevTex4

Scientific paper

10.1016/j.jsv.2004.06.009

We apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincare (``distorted time'') method to find improved approximate solutions to nonlinear problems. We find that our method works very well for a wide range of parameters in the case of the anharmonic oscillator (Duffing equation) and of the non-linear pendulum. The approximate solutions found with this method are better behaved and converge more rapidly to the exact ones than in the simple Lindstedt-Poincar\'e method.

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