Improved Lindstedt-Poincaré method for the solution of nonlinear problems. (English) Zbl 1237.70097

Summary: We apply the Linear Delta Expansion (LDE) to the Lindstedt-Poincaré (“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), of the non linear pendulum and of more general anharmonic potentials. The approximate solutions found with this method converge more rapidly to the exact ones than in the simple Lindstedt-Poincaré method.


70K60 General perturbation schemes for nonlinear problems in mechanics
34E05 Asymptotic expansions of solutions to ordinary differential equations
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