Padé Approximant

An analytical solution using homotopy analysis method is developed to describe the non-8 linear progressive waves in water of finite depth. The velocity potential of the wave is ex-9 pressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by 10 continuous mapping. Unlike the perturbation method, the present approach is not dependent 11 on small parameters. Thus solutions are possible for steep waves. Furthermore, a significant 12 improvement of the convergence rate and region is achieved by applying Homotopy-Padé 13 Approximants. The calculated wave characteristics of the present solution agree well with 14 previous numerical and experimental results.

In this paper the acceleration motion of a vertically falling spherical particle in incompressible Newtonian media is investigated. The velocity is evaluated by using homotopy perturbation method (HPM) and Padé approximant which is an analytical solution technique. The current results are then compared with those derived from HPM and the established fourth order Runge-Kutta method in order to verify the accuracy of the proposed method. It is found that this method can achieve more suitable results in comparison to HPM.

This paper deals with the parabolic formulation of propagation equations of gravity waves in surface in terms of angular capability with respect to the privileged propagation direction. This parabolic formulation is obtained by splitting the Berkhoff equation operator into two ...