At present, three numerical solution methods have mainly been used to solve fractional-order chaotic systems in the literature: frequency domain approximation, predictor–corrector approach and Adomian decomposition method (ADM). Based on literature, ADM is capable of dealing with linear nonlinear problems a time domain. Also, (ADM) among efficient approaches for solving non-linear equations. Nu...

Some of the most common problems in applied sciences and engineering are usually formulated as singular two-point boundary value problems. A well known fact is that the exact solutions in closed form of such problems were not obtained in many cases. In this paper, the exact solutions for a wide class of singular two-point boundary value problems are obtained by using Adomian decomposition method.

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. ...

In this paper, by introducing the fractional derivative in the sense of Caputo, the Adomian decomposition method is directly extended to study the coupled Burgers equations with timeand space-fractional derivatives. As a result, the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components. The figures show the effectiveness and good acc...

Two super cubic convergence methods to solve systems of nonlinear equations are presented. The first method is based on the Adomian decomposition method. We state and prove a theorem which shows the cubic convergence for this method. But numerical examples show super cubic convergence. The second method is based on a quadrature formulae to obtain the inverse of Jacobian matrix. Numerical exampl...

design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.

The Adomian’s decomposition method (ADM) is a solution method with a wide range of applications including the solution of algebraic, differential, integral and integro-differential equations or system of equations. This method was first introduced by Adomian [1, 2] in the beginning of the 1980’s. In this method the solution is considered as an rapidly converging, infinite series. The convergenc...

In this paper, we have discussed the integrability of a nonlinear partial differential equation, with a focus on the Painlevé property, the compatibility condition and the Bäcklund transformation. Afterwards, the Adomian decomposition method, which accurately computes the series solution, has been used to obtain an approximate solution. The convergence analysis based on the wave number and nonl...

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...