Mass, Momentum and Energy Flux in Nonlinear Water Wave Based on HAM Solution

In this paper, the Homotopy Analysis Method (HAM) is applied to solve the fully nonlinear partial differential equation for the steady propagating periodic gravity wave of finite water depth. The series solution of the wave elevation and the velocity potential function are obtained. And then the velocity and pressure fields are plotted and discussed carefully. In order to overcome the drawback of the integral calculations with complex free surface elevation, the discrete integration and fitting procedure based on high-order Fourier series is developed. Based on the accurate HAM solution and fitting technique, the mass, momentum and energy conservation equations are validated. At last, the corresponding mean fluxes are calculated and the velocities of the mass transport and energy transport are supplied accurately.

A Note on Solutions of the SIR Models of Epidemics Using HAM

Recently, Awawdeh et al. (2009) discussed the solutions of SIR epidemics model using homotopy analysis method. This comment points out some crucial flaws in (Awawdeh et al. 2009). Particularly, results presented in Figure 1 of the (Awawdeh et al. 2009) do not represent the 20 term solution of the considered problem as stated. The present paper also provides a new approach for solving SIR epidemics model using homotopy analysis method. The new approach is based on dividing the entire domain into subintervals. In each subinterval the three-term HAM solution is sufficient for obtaining accurate and convergent results. The comparison of the obtained solution using new approach is made with the numerical results and found in excellent agreement.