Most scientists believe that the combination of numerical and semi-exact analytical methods can also end with useful results. Recently, several approximate methods have been developed to analyze the nonlinear problems [112]. Homotopy analysis method (HAM) which was recently developed by [13] is one of the most successful and efficient methods in solving non-linear equations. In comparison with ...

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the eciency of the mentioned algorithm and the h-curve is plotted to determine the region ...

Most of the phenomena of various fields of applied sciences are nonlinear problems. Recently, various types of analytical approximate solution techniques were introduced and successfully applied to the nonlinear differential equations. One of the aforementioned techniques is the Homotopy analysis method (HAM). In this study, we applied HAM to find critical buckling load of a column under end lo...

Homotopy Analysis Transform Method (HATM) is applied to tackle timespace fractional Gas dynamics equation. The proposed HATM is an elegant coupling of homotopy analysis method (HAM) and Laplace transform. The method gives an analytical solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. The numerical solutions obtained...

We have used the homotopy analysis method (HAM) to obtain solution of Davey-Stewartson equations of fractional order. The fractional derivative is described in the Caputo sense. The results obtained by this method have been compared with the exact solutions. Stability and convergence of the proposed approach is investigated. The effects of fractional derivatives for the systems under considerat...

The homotopy analysis method (HAM) is sharpened to solve the Thomas–Fermi equation. Some techniques are employed, including the use of asymptotic analysis to introduce proper transformation, and the use of optimal initial guess and optimal auxiliary linear operator to accelerate the convergence of homotopy approximations. The optimal convergence control parameters are determined by the minimum ...

Abstract— In this paper, we have applied an accurate and efficient homotopy analysis method (HAM) to find the approximate/analytical solutions for space and time fractional reactiondiffusion equations arising in mathematical chemistry. The method provides solutions in rapid convergence series with computable terms. To the best of our knowledge, until now there is no rigorous HAM solutions have ...

In this paper, the basic ideas of a new kind of analytical technique, namely the Homotopy Analysis Method (HAM), are briefly described. Different from perturbation techniques, the HAM does not depend on whether or not there exist small parameters in nonlinear equations under consideration. Therefore, it provides us with a powerful tool to analyse strongly nonlinear problems. A simple but typica...

In this study, the concept of Homotopy analysis method (HAM) is briefly introduced. Furthermore some non-linear problems are handled and the solutions of these problems are given using by HAM, DTM, ADM methods and the convergence of the solution is shown to the exact solution. Additionally, the three methods are compared and it is observed that the HAM is more-less efficient and effective than ...