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An Elementary Solution to a Duffing Equation [PDF]
The Scientific World Journal, 2022 In this work, we study the Duffing equation. Analytical solution for undamped and unforced case is provided for any given arbitrary initial conditions.
Alvaro H. Salas
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Analytical Solution to the Generalized Complex Duffing Equation [PDF]
The Scientific World Journal, 2022 Future scientific and technological evolution in many areas of applied mathematics and modern physics will necessarily depend on dealing with complex systems.
Alvaro H. Salas S +2 more
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Solution to a Damped Duffing Equation Using He’s Frequency Approach [PDF]
The Scientific World Journal, 2022 In this paper, we generalize He’s frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt–Poincaré method.
Alvaro H. S. Salas +2 more
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Locally Exact Integrators for the Duffing Equation [PDF]
Mathematics, 2020 A numerical scheme is said to be locally exact if after linearization (around any point) it becomes exact. In this paper, we begin with a short review on exact and locally exact integrators for ordinary differential equations.
Jan L. Cieśliński, Artur Kobus
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Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities [PDF]
, 2007 We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered T-periodic solutions.
Chen, Hongbin, Li, Yi
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On the Dirichlet problem for a Duffing type equation
Electronic Journal of Qualitative Theory of Differential Equations, 2011 We use direct variational method in order to investigate the dependence on parameter for the solution for a Duffing type equation with Dirichlet boundary value conditions.
Marek Galewski
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Advances in Mathematical Physics, 2021 Based on the study of the feature extraction algorithm based on the multiple empirical mode decomposition of the Duffing equation, this paper proposes a corresponding improved algorithm, completes the identification and analysis of the psychological ...
Min Chai, Lei Ba
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Applied Mathematics in Science and Engineering, 2023 The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as its polarization, dispersion, and interactions with other waves or boundaries.
Mahdi Rakah +4 more
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Results in Physics, 2021 Because the Duffing equation is very sensitive to weak signals and noise immunity, the modified Duffing detection system is applied to detect the weak nonlinear signal in nonlinear ultrasonic experiment.
Yuhua Zhang, Silong Quan, Guoquan Liu
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Analytical Solution for the Cubic-Quintic Duffing Oscillator Equation with Physics Applications
Complexity, 2022 The nonlinear differential equation governing the periodic motion of the one-dimensional, undamped, and unforced cubic-quintic Duffing oscillator is solved exactly by obtaining the period and the solution.
Alvaro H. Salas +2 more
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