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

Modified homotopy perturbation method for solving non-linear Fredholm integral equations

A numerical solution for solving non-linear Fredholm integral equations is presented. The method is based upon homotopy perturbation theory. The result reveal that the modified homotopy perturbation method (MHPM) is very effective and convenient. 2007 Elsevier Ltd. All rights reserved.

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.  

Modified homotopy perturbation method for solving non-linear oscillator's ‎equations

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

Convergence of an Approach for Solving Fredholm Functional Integral Equations

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.

An improvement to the homotopy perturbation method for solving integro-differential equations

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...