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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

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