In this paper, it is revealed that Adomian decomposition method corresponds to Taylor series method when applied to the solution of nonlinear initial value problems, in the following sense: the Adomian ́s polynomials can be obtain trough Taylor coefficients.

In this work, conduction-convection heat transfer through a straight fin, property distribution due to convection-diffusion, and conduction heat transfer through a slab with temperature dependent thermal conductivity are evaluated using Adomian decomposition method. The results are compared with numerical and exact solutions. It is shown that the numerical simulation has some limitations and ma...

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 the conve...

Decomposition method was first introduced by Adomian since the beginning of the 1980’s for solving wide range of problems whose mathematical models yield equation or system of equation involving algebraic, differential, integral and integro-diffrential [1, 2, 3]. This iterative method has been proven to be rather successful in dealing with linear problems as well as nonlinear. Adomian gives the...

By introducing the fractional derivatives in the sense of caputo, we use the Adomian decomposition method to construct the approximate solutions for some fractional partial differential equations with time and space fractional derivatives via the time and space fractional derivatives wave equation, the time and space fractional derivatives reduced wave equation and the (1+1)-dimensional Burger’...

In this paper a recurrence technique for calculating Adomian polynomials is proposed, the convergence of the series for the Adomian polynomials is discussed, and the dependence of the convergent domain of the solution's decomposition series P 1 n¼0 u n on the initial component function u 0 is illustrated. By introducing the index vectors of the Adomian polynomi-als the recurrence relations of t...

In this paper, we developed a new variational iteration method using the quasilinearization and Adomian polynomial to solve nonlinear differential equations. The convergence analysis of our is also discussed under Lipschitz continuity condition in Banach space. Some application problems are included test efficacy proposed method. behavior investigated for different values parameter t. This powe...

In this paper, the Adomian decomposition method for the approximate solution of generalized Korteweg de Vries equation with boundary conditions is implemented. By using this method, the solution is calculated in the form of power series. The method does not need linearization, weak nonlinearity or perturbation theory. By using Mathematica Program, Adomian polynomials of the obtained series solu...