the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to...

With the development of economy, energy systems have become focus academia and industry. The integrated system formed by electricity, gas, heat networks can improve utilization efficiency energy. Heating in play an important role. consideration dynamic characteristics heating network flexibility reduce operation cost system. In this paper, a thermal circuit model is derived for from electrical-...

To find the explicit solutions of nonlinear differential equations, many powerful methods have been used (Abbasbandy, 2006; He, 1998; Wazwaz, 1997; Ghasemi et al., 2007; Adomian and Adomian, 1984). The homotopy analysis method (HAM) (Liao, 2003, 2004; Liao and Tan, 2007; Yamashita et al., 2007) is a general analytic approach to get series solutions of various types of nonlinear equations. The H...

In this paper, the Adomian decomposition method (ADM) is applied to obtain the approximate solution of a mathematical model of carcinogenesis which is a Riccati differential equation derived by Moolgavkar and Venzon (see [9]). The numerical solution obtained by this way have been compared with the exact solution which obtained by Moolgavkar and Venzon (see [11]). This comparison show that the (...

Since 2001, Laplace decomposition algorithm (LDA) has been one of the reliable mathematical methods for obtaining exact or numerical approximation solutions for a wide range of nonlinear problems. The Laplace decomposition algorithm was developed by Khuri in [2] to solve a class of nonlinear differential equations. The basic idea in Laplace decomposition algorithm, which is a combined form of t...

The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...

In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply. 

in this paper, we present a comparative study between the adomian decomposition method and two classical well-known runge-kutta and central difference methods for the solution of damped forced oscillator problem. we show that the adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.