Optimal Homotopy Asymptotic and Homotopy Perturbation Methods for Linear Mixed Volterra-Fredholm Integral Equations

T-Stability Approach to the Homotopy Perturbation Method for Solving Fredholm Integral Equations

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...

Homotopy approximation technique for solving nonlinear‎ ‎Volterra-Fredholm integral equations of the first kind

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...

The comparison of optimal homotopy asymptotic method and homotopy perturbation method to solve Fisher equation

In recent years, numerous approaches have been applied for finding the solutions of functional equations. One of them is the optimal homotopy asymptotic method. In current paper, this method has been applied for obtaining the approximate solution of Fisher equation. The reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

A NEW MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING LINEAR SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.