Two Modifications of the Homotopy Perturbation Method for Nonlinear Oscillators
Naveed Anjum, Ji‐Huan He
Abstract
Nonlinear vibration arises in engineering and physics, and the periodic motion of these nonlinear oscillatory systems have rich dynamics. An estimation of amplitude-frequency relationship of a nonlinear oscillator is much needed, therefore, well-known homotopy perturbation method is employed for this purpose. In this paper, two last modifications of the homotopy perturbation method are briefly reviewed, which couples with either the parameter-expansion technology or the enhanced perturbation method. Both modifications are extremely effective for nonlinear oscillators, and the cubic-quintic-septic Duffing oscillator is used as an example to elucidate the solution processes.
Topics & Concepts
Homotopy perturbation methodNonlinear systemHomotopy analysis methodPerturbation (astronomy)HomotopyMathematicsApplied mathematicsTopology (electrical circuits)Control theory (sociology)PhysicsComputer sciencePure mathematicsQuantum mechanicsCombinatoricsArtificial intelligenceControl (management)Fractional Differential Equations SolutionsModel Reduction and Neural NetworksAdvanced Adaptive Filtering Techniques