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This study analyzes the undamped Duffing oscillator, a nonlinear dynamical system, using an improved version of the Lindstedt Poincare method (LPM). The researchers demonstrate that their proposed modification achieves better convergence compared to both the standard LPM and Burton's modified version when validated against numerical solutions obtained through higher-order Runge-Kutta methods.
Why it matters
The Duffing oscillator has wide-ranging applications in physics, engineering, and biological systems. Improved analytical methods for solving such nonlinear systems can enhance modeling accuracy and computational efficiency in practical applications across these fields.
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arXiv:2607.15233v1 Announce Type: cross
Abstract: The undamped Duffing oscillator is a nonlinear dynamical system with broad applications in physics, engineering and biological system. We present a comprehensive analysis of this system using the Lindstedt Poincare method (LPM) and its modifications and make comparison with numerical solution obtained using higher order Runge-Kutta. It is also shown the method suggested in this article converges better than the standard LPM and Lindstedt Poincare method with Burton’s modification.
Source: Study of Duffing oscillator using an improved Lindstedt Poincare method and relevant comparisons