A homotopy technique and a perturbation technique for non-linear problems

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...

VARIATIONAL HOMOTOPY PERTURBATION METHOD FOR SOLVING THE NONLINEAR GAS DYNAMICS EQUATION

A. Noor et al. [7] analyze a technique by combining the variational iteration method and the homotopy perturbation method which is called the variational homotopy perturbation method (VHPM) for solving higher dimensional initial boundary value problems. In this paper, we consider the VHPM to obtain exact solution to Gas Dynamics equation.

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Nonlinear stability of rotating two superposed magnetized fluids with the technique of the homotopy perturbation

In the present work, the Rayleigh-Taylor instability of two rotating superposed magnetized fluids within the presence of a vertical or a horizontal magnetic flux has been investigated. The nonlinear theory is applied, by solving the equation of motion and uses the acceptable nonlinear boundary conditions. However, the nonlinear characteristic equation within the elevation parameter is obtained....

Modified homotopy method to solve non-linear integral equations

In this article we decide to define a modified homotopy perturbation for solving non-linear integral equations. Almost, all of the papers that was presented to solve non-linear problems by the homotopy method, they used from two non-linear and linear operators. But we convert a non-linear problem to two suitable non-linear operators also we use from appropriate bases functions such as Legendre ...

Solving the non linear system of third order boundary value problems by using He's homotopy perturbation method