Exact solutions for nonlinear integral equations by a modified homotopy perturbation method

Exact Solutions for Systems of Volterra Integral Equations of the First Kind by Homotopy Perturbation Method

In this article, the homotopy perturbation method is proposed to solve systems of Volterra integral equations of the first kind. Theoretical proposes are presented briefly, so that this paper can be read independently. To illustrate the method some examples are presented. The results reveal that the homotopy perturbation method is very effective and simple and gives the exact solutions.

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...

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

A Modified Homotopy Perturbation Method for Solving Linear and Nonlinear Integral Equations

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...

Exact solutions of nonlinear interval Volterra integral equations