On Adomian's decomposition method and some comparisons with Picard's iterative scheme
Nicola Bellomo,D. Sarafyan +1 more
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In this article, the authors consider the general mathematical framework of Adomian's decomposition method for a large class of nonlinear operator equations and compare it with Picard's iterative scheme for the same class of equations.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1987-05-01 and is currently open access. It has received 35 citations till now. The article focuses on the topics: Adomian decomposition method & Decomposition method (queueing theory).read more
Citations
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A review of the decomposition method in applied mathematics
TL;DR: The decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions, closure approximations, perturbation theory, or restrictive assumptions on stochasticitiy as mentioned in this paper.
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A review of the decomposition method and some recent results for nonlinear equations
TL;DR: The decomposition method can be an effective procedure for solution of nonlinear and/or stochastic continuous-time dynamical systems without usual restrictive assumptions as mentioned in this paper, which is intended as a convenient tutorial review of the method.
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A review of the decomposition method and some recent results for nonlinear equations
TL;DR: The decomposition method can be an effective procedure for solution of nonlinear and/or stochastic continous-time dynamical systems without usual restrictive assumptions as discussed by the authors, which is intended as a convenient tutorial review of the method.
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Recurrence triangle for Adomian polynomials
TL;DR: The method simplifies the computation of the Adomian polynomials and illustrates by examples that the domain of convergence can be changed by choosing a different u"0 and a modified iteration.
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Convergence of the Adomian decomposition method for initial‐value problems
TL;DR: In this paper, the authors 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.
References
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The Boltzmann equation. I. Uniqueness and local existence
Shmuel Kaniel,Marvin Shinbrot +1 more
TL;DR: In this paper, an abstract form of the spatially nonhomogeneous Boltzmann equation is derived which includes the usual, more concrete form for any kind of potential, hard or soft, with finite cutoff.
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A comparison between Adomian's decomposition methods and perturbation techniques for nonlinear random differential equations
Nicola Bellomo,Roberto Monaco +1 more
TL;DR: In this paper, a comparison of the Adomian decomposition method and regular perturbation techniques applied to the solution of nonlinear vector random differential equations is made. And the comparison shows that the decomposition is easier to compute and supplies quantitatively reliable results.
Book
Partial Differential Equations: New Methods for Their Treatment and Solution
Richard Bellman,George Adomian +1 more
TL;DR: In this paper, the authors present an approach to the problem of finding a solution for the discrete approximation problem in the context of the Calculus of Variations, which is a generalization of the calculus of variations.
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Solutions of nonlinear boundary value problems by the decomposition method
D. Bigi,R. Riganti +1 more
TL;DR: In this article, a method for determining boundary value problems in nonlinear operator equations based on the Adomian decomposition procedure is proposed, which is applied with satisfactory results to the study of a classical boundary value problem in continuum mechanics.