Homotopy Perturbation Method with an Auxiliary Term

By Ji-Huan He. 2012

134 citations recorded by the source corpus.

The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d72a63ceda8bf57556f47502c6ed1b165a50aa40

Citations in the corpus

• A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “The homotopy perturbation method was originally proposed to nonlinear differential equations [76–79].”
• The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators (2019, unknown): “He’s frequency formulation was initially inspired by an ancient Chinese algorithm36; now this formulation has gained much attention and has been under development, with various modifications appearing in open literature.37–45 We define a residual function R(t) as RðtÞ ¼ u00 þ fðuÞ (7) He’s frequency”