Homotopy perturbation method with three expansions for Helmholtz-Fangzhu oscillator
Ji‐Huan He, Yusry O. El‐Dib
Abstract
This paper shows that the Toda oscillator can be converted to a new Helmholtz-Fangzhu equation, which is solved by the homotopy perturbation method with three expansions. The solution, the negative frequency and the damping rate are expanded into power forms in the homotopy parameter, the solution process is given step by step, and the results are of high accuracy. This paper gives a general approach to damp vibrations with singular terms,especially to the Helmholtz-Fangzhu oscillator.
Topics & Concepts
Homotopy perturbation methodHelmholtz free energyHelmholtz equationHomotopy analysis methodPerturbation (astronomy)HomotopyVibrationMathematical analysisPerturbation theory (quantum mechanics)MathematicsPhysicsApplied mathematicsQuantum mechanicsPure mathematicsBoundary value problemFractional Differential Equations SolutionsAcoustic Wave Phenomena ResearchNumerical methods in engineering