Presenting a new method for the solution of nonlinear problems

Abstract

We present a method for the resolution of (oscillatory) nonlinear problems. It is based on the application of the Linear Delta Expansion to the Lindstedt-Poincaré method. By applying it to the Duffing equation, we show that our method substantially improves the approximation given by the simple Lindstedt-Poincaré method.

12 pages, 3 figures. LATEX

References in corpus (5)

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• High Temperature Resummation in the Linear $\delta$-Expansion
• Optimized $\delta$ expansion for the Walecka model
• Quantum Dynamics of the Slow Rollover Transition in the Linear Delta Expansion
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• Comparison of alternative improved perturbative methods for nonlinear oscillations
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• High order analysis of nonlinear periodic differential equations
• A new method for the solution of the Schrodinger equation
• Systematic perturbation calculation of integrals with applications to physics
• The period of a classical oscillator
• Periods of relativistic oscillators with even polynomial potentials
• Convergence acceleration of series through a variational approach
• Dispersion relation of the non-linear Klein-Gordon equation through a variational method
• Analytical Approximate Solution of a Coupled Two Frequency Hill's Equation
• A comparative study of some analytic approximate methods for the anharmonic oscillator described by cubic quartic potential