Please use this identifier to cite or link to this item:
http://hdl.handle.net/11375/21346
Title: | Adomian Decomposition Method: Convergence Analysis and Numerical Approximations |
Authors: | Abdelrazec, Ahmed |
Advisor: | Pelinovsky, Dmitry |
Department: | Mathematics |
Keywords: | Adomian;Decomposition;convergence analysis;Numerical Approximations |
Publication Date: | Nov-2008 |
Abstract: | 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. We outline some substantial differences between the two methods and show that the decomposition method converges faster than the Picard method. Several nonlinear differential equations are considered for illustrative purposes and the numerical approximations of their solutions are obtained using MATLAB. The numerical results show how the decomposition method is more effective than the standard ODE solvers. Moreover, we prove convergence of the ADM for the partial differential equations and apply it to the cubic nonlinear Schrodinger equation with a localized potential. |
URI: | http://hdl.handle.net/11375/21346 |
Appears in Collections: | Digitized Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Abdelrazec_Ahmed_H_M_2008Nov_Masters.pdf | 2.96 MB | Adobe PDF | View/Open |
Items in MacSphere are protected by copyright, with all rights reserved, unless otherwise indicated.