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...

the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.

The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system ...

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability. Keywords—Fuzzy-valued function, Fuzzy initial value...

the main purpose of this paper is to consider adomian's decomposition method in non-linear volterra integro-differential equations. the advantages of this method, compared with the recent numerical techniques (in particular the implicitly linear collocation methods) , and the convergence of adomian's method applied to such nonlinear integro-differential equations are discussed. finall...

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...

We prove convergence of the Adomian decomposition method for an abstract initial-value problem using the method of majorants from the Cauchy-Kowalevskaya theorem for differential equations with analytic vector fields. Convergence rates of the Adomian method are investigated in the context of the nonlinear Schrödinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq...

in this paper, a practical review of the adomian decomposition method, to extend the procedure to handle the strongly nonlinear problems under the mixed conditions, is given and the convergence of the algorithm is proved. for this respect, a new and simple way to generate the adomian polynomials, for a general nonlinear function, is proposed. the proposed procedure, provides an explicit formula...

Abstract The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic (MHD) incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the Variational iteration method (VIM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM). In the paper, our result...

The Adomian decomposition method (ADM) and high-pass filters are employed in this study to investigate the free vibrations and damage detection of cracked Euler-Bernoulli beams. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the mode shapes can be determined for beams consisting of an arbitrary number of cracks under general boundary condi...