Adomian Decomposition Method and Padé Approximants for Nonlinear Differential-Difference Equations

2009 ◽  
Vol 51 (4) ◽  
pp. 581-587
Author(s):  
Liu Yan-Ming ◽  
Chen Yong
2021 ◽  
pp. 2150038
Author(s):  
Man Kwong Mak ◽  
Chun Sing Leung ◽  
Tiberiu Harko

The Schrödinger–Newton system is a nonlinear system obtained by coupling together the linear Schrödinger equation of quantum mechanics with the Poisson equation of Newtonian mechanics. In this work, we will investigate the effects of a cosmological constant (dark energy or vacuum fluctuation) on the Schrödinger–Newton system, by modifying the Poisson equation through the addition of a new term. The corresponding Schrödinger–Newton-[Formula: see text] system cannot be solved exactly, and therefore for its study one must resort to either numerical or semianalytical methods. In order to obtain a semianalytical solution of the system we apply the Adomian Decomposition Method, a very powerful method used for solving a large class of nonlinear ordinary and partial differential equations. Moreover, the Adomian series are transformed into rational functions by using the Padé approximants. The semianalytical approximation is compared with the exact numerical solution, and the effects of the dark energy on the structure of the Newtonian quantum system are fully investigated.


2013 ◽  
Vol 18 (3) ◽  
pp. 935-943
Author(s):  
O.D. Makinde ◽  
U.S. Mahabaleswar ◽  
N. Maheshkumar

Abstract In this paper, the Adomian decomposition method with Padé approximants are integrated to study the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field. A closed form power series solution based on Adomian polynomials is obtained for the similarity nonlinear ordinary differential equation modelling the problem. In order to satisfy the farfield condition, the Adomian power series is converted to diagonal Padé approximants and evaluated. The results obtained using ADM-Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily employed to solve a wide range of nonlinear boundary value problems


Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6269-6280
Author(s):  
Hassan Gadain

In this work, combined double Laplace transform and Adomian decomposition method is presented to solve nonlinear singular one dimensional thermo-elasticity coupled system. Moreover, the convergence proof of the double Laplace transform decomposition method applied to our problem. By using one example, our proposed method is illustrated and the obtained results are confirmed.


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