In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

Nonlinear functional integral equations have been discussed in the literature extensively, for a long time. See for example, Subramanyam and Sundersanam [15], Ntouyas and Tsamatos [14], Dhage and Regan [10] and the references therein, Recently, the present author, in a series of papers [4, 6] initiated the study of nonlinear integral equations in a Banach algebra via fixed point techniques. In ...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

Although perturbation techniques are widely applied to analyze nonlinear problems in science and engineering, they are however so strongly dependent on small parameters appeared in equations under consideration that they are restricted only to weakly nonlinear problems. For strongly nonlinear problems which don’t contain any small parameters, perturbation techniques are invalid. So, it seems ne...

the first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. this method can be applied to non integrable equations as well as to integrable ones. in this paper, the first integral method is used to construct exact solutions of the 2d ginzburg-landau equation.

in this paper, using the tools involving measures of noncompactness and darbo fixed point theorem forcondensing operator, we study the existence of solutions for a large class of generalized nonlinear quadraticfunctional integral equations. also, we show that solutions of these integral equations are locally attractive.furthermore, we present an example to show the efficiency and usefulness of ...

in this paper, we studied the numerical solution of nonlinear weakly singular volterra-fredholm integral equations by using the product integration method. also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear volterra-fredholm integral equations. the reliability and efficiency of the proposed scheme are...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...