In this paper, we apply homotopy analysis method (HAM) for computing the eigenvalues of SturmLiouville problems. The parameter h, in this method, helps us to adjust and control the convergence region. The results show that this method has validity and high accuracy with less iteration number in compare to Variation Iteration Method (VIM) and Adomian decomposition method (ADM). Moreover it is il...

In this paper, the homotopy analysis method (HAM) is applied to solve a parameterized sixth order boundary value problem which, for large parameter values, cannot be solved by other analytical methods for finding approximate series solutions. Convergent series solutions are obtained, no matter how large the value of the parameter is.

In this paper, the homotopy analysis method (HAM) which is a powerful technique of nonlinear analysis, is examined in the solution of the linear vibration equation for very a large circular membrane. The method is shown to be able to handle a variety of pertaining singular boundary value problems (BVPs), to allow for graphical presentation of the results, and appears to be a viable alternative ...

In this paper, the nonlinear dynamical systems are solved by using the homotopy analysis method (HAM).The approximation solution of this equation is calculated in the form ofa series which its components are computed easily. The existence anduniqueness of the solution and the convergence of the proposed methodare proved.The results obtained here demonstrate that the HAM is an effective and robu...

In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these hig...

The homotopy analysis method (HAM) is a useful to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein–Weyl coupled with Maxwell field and obtain approximation for charged by using HAM. It found that are sufficiently accurate entire spacetime outside hole’s event horizon also consistent numerical ones Einstein–Maxwell–Weyl gra...

The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically w...

In this study, accurate analytical solution for the nonlinear free vibration of an oscillator with inertia and static type cubic nonlinearities is derived. This solution is called He’s Variational Iteration Method (VIM). Comparing this method with numerical integration solutions using a built-in ODE-solver in MATLAB and He’s Homotopy Analysis Method (HAM) is shown its drastic approximation. By ...

In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical solution of the model in fractional order. The obtained results are compared with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer ca...

In this paper, an iterative scheme based on the homotopy analysis method (HAM) has been used to solve nonlinear integral equations. To check the numerical method, it is applied to solve different test problems with known exact solutions and the numerical solutions obtained confirm the validity of the numerical method and suggest that it is an interesting and viable alternative to existing numer...