in this paper, we have tried to find a solution for quick transfer of nuclear wastes from pools of cool water to dry stores to reduce the environmental concerns and financial cost of burying atomic waste. therefore, the rate of heat transfer from atomic waste materials to the outer surface of the container should be increased. this can be achieved by covering the bottom of the pool space with c...

Path tracking is the fundamental computational tool in homotopy continuation and is therefore key in most algorithms in the emerging field of numerical algebraic geometry. Though the basic notions of predictor-corrector methods have been known for years, there is still much to be considered, particularly in the specialized algebraic setting of solving polynomial systems. This article considers ...

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...

The steady flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation is studied. We present a novel technique for accelerating the convergence of the spectral-homotopy analysis method. Solutions of the nonlinear momentum and energy equations are obtained using the improved spectral homotopy analysis method. Solutions were also generated using the spectral-homotopy analysis method...

in this paper, a fuzzy hunter-saxton equation is solved by using the adomian'sdecomposition method (adm) and homotopy analysis method (ham). theapproximation solution of this equation is calculated in the form of series whichits components are computed by applying a recursive relation. the existenceand uniqueness of the solution and the convergence of the proposed methodsare proved. a nume...

In this paper, we apply He’s semi-inverse method to establish a variational theory for the Boussinesq system. Based on this formulation, a solitary solution can be easily obtained using Ritz method. Moreover, the results are also compared with He’s homotopy perturbation method, Liao’s homotopy analysis method and homotopy padémethod. The results reveal that the proposed method is very effective...

In this paper, we present homotopy perturbation method (HPM) for solving the Korteweg-de Vries (KdV) equation and convergence study of homotopy perturbation method for nonlinear partial differential equation. We compared our solution with the exact solution and homotopy analysis method (HAM). The results show that the HPM is an appropriate method for solving nonlinear equation.

A new definition of the homotopy analysis method is given by means of the decomposition method in this paper. The convergence of the homotopy decomposition method is proved under some reasonable hypotheses, which provide the theoretical basis of the homotopy decomposition method for solving nonlinear problems. AMS subject classification: 34A34.