In this article the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. Mathematical modeling of the problem leads to a system of non-linear ordinary differential equations. Adomian decomposition method is employed to solve this system of nonlinear ordinary differential equations, the problem of conve...

In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of...

First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...

In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integrodifferential equation by using the following powerful, efficient but simple methods: (i) Modified Adomian decomposition method (MADM), (ii) Variational iteration method (VIM), (iii) Homotopy analysis method (HAM) and (iv) Modified homotopy perturbation method (MHPM). The uniqueness of the solution and the conve...

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful al...

Aim of the paper is to investigate applications of Homotopy Perturbation Method(HPM) on non-linear physical problems .Some coupled non-linear partial differential equations are considered and solved numerically using Homotopy Perturbation Method. The results obtained by HPM are compared with those obtained by Adomian Decomposition Method. The behavior of Homotopic solution is shown through grap...

A generalized Fisher’s equation is solved by using the modified Adomian decomposition method MADM , variational iteration method VIM , homotopy analysis method HAM , and modified homotopy perturbation method MHPM . The approximation solution of this equation is calculated in the form of series whose components are computed easily. The existence, uniqueness, and convergence of the proposed metho...

In this paper, Adomian decomposition method is applied to solve system linear fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Special attentions are given to study the convergence of the proposed method. Finally, some numerical examples are provided to show that this method is computationally efficient. Refer ences A. Arikoglu, and I. Ozko...

This article presents an iterative scheme for solution of the viscous Cahn-Hilliard equation. The procedure is based on the Variational Iteration Method (VIM) in which the solutions are calculated in the form of a convergent series with easily computable components. A good agreement is observed between the present solutions and that obtained by other iterative methods like Adomian Decomposition...

In this paper, we present the exact solutions of the partial differential equations in different dimensions with variable coefficients by using the homotopy perturbation method. The feature of this method is its flexibility and ability to solve parabolic-like equations and hyperbolic-like equations without the calculation of complicated Adomian polynomials or unrealistic nonlinear assumptions. ...