Solutions of the force-free Duffing-van der Pol oscillator equation

DOI10.1155/2011/852919zbMath1239.34015OpenAlexW1977392020WikidataQ58686849 ScholiaQ58686849MaRDI QIDQ762992

Syed Anwar Ali, Najeeb Alam Khan, Nadeem Alam Khan, Muhammad Kamran Jamil

Publication date: 8 March 2012

Published in: International Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2011/852919

zbMATH Keywords

Padé approximantsLaplace transformationhomotopy series

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (5)

Hermite Functional Link Neural Network for Solving the Van der Pol–Duffing Oscillator Equation ⋮ Dynamic analysis of rotating pendulum by Hamiltonian approach ⋮ On the integrability of Liénard i-type equations via \(\lambda \)-symmetries and solvable structures ⋮ First integrals and analytical solutions of some dynamical systems ⋮ Analytical solutions of nonlinear system of fractional-order van der Pol equations

Cites Work

• On efficient method for system of fractional differential equations
• An efficient approach for solving the Riccati equation with fractional orders
• A reliable aftertreatment for improving the differential transformation method and its application to nonlinear oscillators with fractional nonlinearities
• Multiple-parameter Hamiltonian approach for higher accurate approximations of a nonlinear oscillator with discontinuity
• Application of a modified He's homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities
• The iterative homotopy harmonic balance method for conservative Helmholtz-Duffing oscillators
• The homotopy perturbation method for nonlinear oscillators with discontinuities.
• Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt--Poincaré method
• Analytical approach to linear fractional partial differential equations arising in fluid mechanics
• Variational approach for nonlinear oscillators
• The variational iteration method for nonlinear oscillators with discontinuities
• A study of nonlinear oscillators with u1/3 force by He's variational iteration method
• Solution of the Duffing–van der Pol oscillator equation by a differential transform method
• Variational approach to the nonlinear oscillator of a mass attached to a stretched wire
• New aspects of integrability of force-free Duffing–van der Pol oscillator and related nonlinear systems

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