Numerical Solution of Non-linear System of Partial Differential Equations by Using HPM Method

In this article, we propose a powerful method called homotopy perturbation method (HPM) for obtaining the analytical solutions for an non-linear system of partial differential equations. We begin this article by apply HPM method for an important models of linear and non-linear partial differential equations.

Existence And Uniqueness Of Strong Solution For A Semi- Linear Wave Equation With Nonlinear Boundary Dissipation

We aim in this research to study the existence and uniqueness of strong solution for initial-boundary values problem for a semi-linear wave equation with the nonlinear boundary dissipation, by transforming it to a Cauchy problem with second order operator differential equations in Hilbert space. Therefore, we transform it, using Green's formula for a triple of Hilbert spaces.

Numerical Solution of Some Important Models of Partial Differential Equations Using Approximate - Analytical Methods ( ADM – VIM )

In this article, powerful approximate analytical methods, called Adomian decomposition method and variational iteration method are introduced and applied to obtaining the approximate analytical solutions for an important models of linear and non-linear partial differential equations such as ( nonlinear Klein Gordon equation - nonlinear wave equation - linear telegraph equation - nonlinear diffusion convection equation ) . The studied examples are used to reveal that those methods are very effective and convenient for solving linear and nonlinear partial differential equations . Numerical results and comparisons with the exact solution are included to show validity, ability, accuracy, strength and effectiveness of those techniques.