In this paper, the homotopy analysis method has been applied to solve (2 + 1)-dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of ...

The homotopy analysis method HAM is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup WBK equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

in this paper, we present an ecient numerical algorithm for solving fuzzy systemsof linear equations based on homotopy perturbation method. the method is discussed indetail and illustrated by solving some numerical examples.

In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...

In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.

Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory. Furthermore, we consider 1-D elliptic type equation to testify that the homotopy regularization can ide...

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...

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...

In many fields of science and engineering, it is needed to find all solutions of mixed trigonometric polynomial systems. Commonly, mixed trigonometric polynomial systems are transformed into polynomial systems by variable substitution and adding some quadratic equations, and then solved by some numerical methods. However, transformation of a mixed trigonometric polynomial system into a polynomi...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...