Improved Lindstedt-Poincare method for the solution of nonlinear problems

Abstract

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-Poincaré method.

24 pages, 7 figures, RevTex4

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• Presenting a new method for the solution of nonlinear problems
• Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem
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