In this paper, Adomian decomposition method (ADM) and homotopy analysis method (HAM) are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind(FV FIE− 2). we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this s...

Applications in physics are modeled by nonlinear systems. Very few nonlinear systems have closed form solutions, therefore, many researchers stress their goals to search numerical solutions. Homotopy analysis method HAM , first proposed by Liao 1 , is an elegant method which has proved its effectiveness and efficiency in solving many types of nonlinear equations 2, 3 . Liao in his book 4 proved...

The homotopy analysis method (HAM) is used to find approximate analytical solutions of continuous population models for single and interacting species. The homotopy analysis method contains the auxiliary parameter ~, which provides us with a simple way to adjust and control the convergence region of series solution. the solutions are compared with the numerical results obtained using NDSolve, a...

In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto–Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series solution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x, t), the initial guess, u0(x, t) and the auxiliary linear...

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...