7 citations · 25 across the 11 of their papers we have counts for
8 papers · 1 filter
Alternative Fourier-series approach to nonlinear oscillations
Francisco M. Fernández
We propose an alternative approach that avoids the nonlinear equations for the Fourier coefficients that appear in the method of harmonic balance. We apply it to two simple illustr…
On a simple approach to nonlinear oscillators
Francisco M. Fernández
We analyze a simple textbook approach to nonlinear oscillators proposed recently, disclose its errors, limitations and misconceptions and complete the calculations that the authors…
Perturbation approaches and Taylor series
Francisco M. Fernandez
We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation…
On the homotopy perturbation method for Boussinesq-like equations
Francisco M. Fernández
We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exa…
The virial theorem for nonlinear problems
Paolo Amore, Francisco M Fernández
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation p…
On some approximate methods for nonlinear models
Francisco M. Fernández
We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment…