Sentence examples for using the homotopy analysis from inspiring English sources

Convergence criteria of series solutions are given by using the homotopy analysis method [23 30].

The second equation has been solved by Das et al. [8] using the homotopy analysis method.

The closed-form expression of the nonlinear free vibration of the pipe was determined using the homotopy analysis method.

Xu and Cang [10] solved the fractional heat-like and wave-like equations with variable coefficients using the homotopy analysis method (HAM).

In this paper, the periodic solutions for the oscillation of a mass attached to a stretched elastic wire are obtained using the homotopy analysis method (HAM).

Geometrically nonlinear free vibrations of symmetric rectangular honeycomb sandwich panels with simply supported boundaries at the four edges are investigated using the homotopy analysis method (HAM).

In this paper, we use the homotopy analysis method to solve the problem.

We have used the Homotopy Analysis Method (HAM) in order to derive analytical solutions both for the amplitude and the temporal average of nonlinear vibrations.

Inc (2008) used the homotopy analysis method to evaluate the efficiency of straight fins with temperature-dependent thermal conductivity and determined the temperature distribution within the fin.

Turkyilmazoglu [13] used the homotopy analysis method to solve the equations governing the flow of a steady, laminar, incompressible, viscous, and electrically conducting fluid due to a rotating disk subjected to a uniform suction and injection through the walls in the presence of a uniform transverse magnetic field.

This fully coupled and highly nonlinear system was solved using the spectral homotopy analysis method and the successive linearisation method.