Adomian Decomposition Method

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The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia.
1.2.2 Adomian Decomposition Method. The Adomian decomposition method, also known as the inverse operator method, is a mathematical method for solving linear and nonlinear mathematical physics equations; it was proposed by George Adomian (1986, 1988, 1994). The basic idea of the Adomian decomposition method is to decompose the unknown equation ... Adomian decomposition of Buckley-Leverett equation. In the Adomian decomposition method, the solution of a given problem is considered as a series solution. Therefore, the water saturation is expressed as. If a functional equation is considered for water saturation, it can be written in the form.
In the 1980t’s, George Adomian (1923–1996) introduced a powerful method for solving nonlinear functional equations. His method is known as the Adomian decomposition method (ADM) . This technique is based on the representation of a solution to a functional equation as series of functions.
The Adomian Decomposition Method (ADM) is a very effective approach for solving broad classes of nonlinear partial and ordinary differential equations, with important applications in different fields of applied mathematics, engineering, physics and biology. It is the goal of the present paper to provide a clear and pedagogical introduction to the Adomian Decomposition Method and to some of its ...
The Adomian decomposition method was introduced and developed by George Adomian and is well addressed in the literature. The Adomian decomposition method has been receiving much attention in recent years in applied mathematics in general, and in the area of series solutions in particular. The method proved to be powerful, effective, and can ...
Adomian Decomposition Method. We illustrate applications of the Adomian decomposition method (ADM for short) by considering nonlinear system of differential equations with two dependent variables: { L 1 [ y 1] = N 1 [ y 1, y 2] + g 1 ( t), L 2 [ y 2] = N 2 [ y 1, y 2] + g 2 ( t), subject to the initial conditions. y 1 ( 0) = y 10, y 2 ( 0) = y 20.
In this paper, we study the Adomian decomposition method (ADM for short) including its iterative scheme and convergence analysis, which is a simple and effective technique in dealing with some nonlinear problems. We take algebraic equations and fractional differential equations as applications to illustrate ADM’s efficiency.
Jun-Sheng Duan, Randolph Rach, Dumitru Baleanu, Abdul-Majid Wazwaz, A review of the Adomian decomposition method and its applications to fractional differential equations, Communications in ...
Now, using Adomian decomposition method, re-write equation (3.1) in the general operator form as. And so in; in this manner the rest of the components of the decomposition series (2.3) can be obtained. The. 4Ltu Lxx u (3.3) 2. solution for the heat (diffusion) equation (3.1) in a seris form is given by.
Adomian decomposition sumudu transform method for solving a solid and porous fin with temperature dependent internal heat generation. Article. Full-text available. Dec 2016. Trushit Patel ...
Abstract. The Adomian decomposition method (ADM) is a method for the solution of both linear and nonlinear differential equations and BVPs seen in different fields of science and engineering . However, the implementation of this method mainly depends upon the calculation of Adomian polynomials for nonlinear operators .
It has been established that the Adomian decomposition method (ADM) is an effective semi-analytical technique for computing an analytic approximate solution to a non-linear equation as an infinite ...
The Adomian decomposition method was first introduced by George Adomian to solve the system of stochastic equations (Adomian, 1980). This decomposition method can be an effective procedure for obtaining analytical solutions without linearization or weak nonlinear assumptions, perturbation theory or restrictive assumptions on
In this paper, we present a numerical method called the Variation iteration Adomian decomposition method (VIADM) for solving nonlinear partial differential equations (PDEs). The method modifies the traditional formulation of the variation iteration decomposition method (VIDM) such that it converges more rapidly to the analytic solution. Also, the present method is explicit as it requires no ...
The Adomian decomposition method (ADM) is a systematic approximation method for solving ordinary and partial nonlinear differential equations. The method is based on the assumption that the solution can be represented by infinite series y ( x) = ? n ? 0 u n ( x). It was named by Richard Bellman in honor of Adomian because it was developed ...
This article deals with two different methods to solve a time fractional partial integro-differential equation. The fractional derivatives are defined here in Caputo sense. The model problem is solved using the Adomian decomposition method and homotopy perturbation method. Moreover, this paper proves the convergence analysis of the solution based on the present methods. Numerical evidences are ...
In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and activity of the proposed technique. This strategy gives a precise and productive system in ...
A New Algorithm for Solving Riccati Equation Using Adomian Decomposition Method by A. Fakharian, M. T. Hamidi Beheshti, M. Najafi Abstract — Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered.
In this research, Adomian decomposition method (ADM) is presented to find the numerical solution of the equations arising in oscillatory motion of a simple pendulum. For comparative study Haar wavelet method (HWM) is utilized. Numerical examples
Adomian Decomposition Method as discussed by Adomian (1986) and Adomian and Cherruault (1993), Adomian and Cherruault (1995) and some important predictions can be made on the basis of the present study. The advantage of decomposition method is to give . analytical approximate solution of nonlinear ordinary or partial differential eq
We prove convergence of the Adomian Decomposition Method (ADM) by using the Cauchy-Kovalevskaya theorem for differential equations with analytic vector fields, and obtain a new result on the convergence rate of the ADM. Picard's iterative method is considered for the same class of equations in comparison with the decomposition method.
This work proposes and investigates the existence and uniqueness of solutions of Riccati Fractional Differential Equation (RFDE) with constant coefficients using Banach’s fixed point theorem. This theorem is the uniqueness theorem of a fixed point on a contraction mapping of a norm space. Furthermore, the combined theorem of the Adomian Decomposition Method (ADM) and Kamal’s Integral ...
Adomian decomposition method. In chapter 4, we review some inverse problems and show how ADM is used for solv-ing these problems. There are many classi cations of the inverse problems, we will deal with boundary conditions determination of inverse problems[31] and parameter
New Modified Variational Iteration Laplace Transform Method Compares Laplace Adomian Decomposition Method for Solution Time-Partial Fractional Differential Equations. Mohamed Z. Mohamed, Tarig M. Elzaki, Mohamed S. Algolam, Eltaib M. Abd Elmohmoud, Amjad E. Hamza. J. Appl. Math. 2021, 1-10, (2021) DOI: 10.1155/2021/6662645.
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Method adomian decomposition nonlinear differential equations solution solving equation partial fractional ordinary equations. george method. series effective present paper convergence using inverse technique applications solve numerical theorem.