n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

Adomian s decomposition method (ADM) is proposed to approximate the numerical and analytical solutions of system two-dimensional Burgers equations (STDBE) with initial conditions. The advantages of this work are the decomposition method reduces the computational work and improvement with regard to its accuracy and rapid convergence. Some examples are given to illustrate the performance of the m...

In the research, nonlinear volterra partial integro-differential equation is considered. This paper compares the Homotopy Perturbation Method (HPM) with Variational Iteration Method (VIM) for solving this equation. Compared with the Adomian Decomposition Method (ADM), the methods used for this equation need less work. The results of applying these methods show the simplicity and efficiency of t...

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

Smoking is a social trend that prevalent around the world, particularly in places of learning and at some significant events. The World Health Organization defines smoking as most important preventable cause disease third major death humans. In order to analyze this matter, study typically emphasizes analyzing dynamics fractional quitting model via Caputo-Fabrizio differential operator. For num...