Journal ArticleDOI
The decomposition method applied to systems of Fredholm integral equations of the second kind
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The Adomian decomposition method is applied to solve systems of linear and nonlinear Fredholm integral equations of the second kind to prove convergence of the method.About:
This article is published in Applied Mathematics and Computation.The article was published on 2004-01-01. It has received 109 citations till now. The article focuses on the topics: Fredholm integral equation & Fredholm theory.read more
Citations
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Journal ArticleDOI
Solving a multi-order fractional differential equation using adomian decomposition
TL;DR: An algorithm has been developed to convert the multi-order fractional differential equation into a system of fractionaldifferential equations and the Adomian decomposition method has been employed to solve the system of fractions.
Journal ArticleDOI
Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition
TL;DR: Adomian decomposition method has been used to obtain solutions of linear/nonlinear fractional diffusion and wave equations and its applications have been presented.
Journal ArticleDOI
The use of the decomposition procedure of Adomian for solving a delay differential equation arising in electrodynamics
Mehdi Dehghan,Fatemeh Shakeri +1 more
TL;DR: In this paper, the authors investigated the convergence of the approach for the pantograph equation using the Adomian decomposition method and established that the approach can reduce the volume of calculations by not requiring discretization of the variables, linearization or small perturbations.
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Solving multi-term linear and non-linear diffusion–wave equations of fractional order by Adomian decomposition method
TL;DR: Multi-term linear and non-linear diffusion–wave equations of fractional order are solved using Adomian decomposition method, and some numerical examples are presented.
Journal ArticleDOI
Convergence of the Adomian method applied to a class of nonlinear integral equations
TL;DR: In this work, a reliable approach for convergence of the Adomian method when applied to a class of nonlinear Volterra integral equations is discussed and is reliable enough to estimate the maximum absolute truncated error of theAdomian series solution.
References
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Book
Computational Methods for Integral Equations
L. M. Delves,J. L. Mohamed +1 more
TL;DR: In this article, the authors introduce the theory of linear integral equations of the second kind and the Nystrom (quadrature) method for Fredholm equations of second kind, and present an analysis of the Galerkin method with orthogonal basis.
Book
Linear stochastic systems
TL;DR: Stochastic Processes Linear Stochastic Systems Estimation Theory Stochastics Realization Theory System Identification: Foundations and Basic Concepts.
Book
Nonlinear Stochastic Systems Theory and Applications to Physics
TL;DR: In this paper, the authors present a decomposition method for differential and partial differential Equations of the An Polynomials for composite nonlinearity and linearization problems.
Journal ArticleDOI
New results for convergence of Adomian's method applied to integral equations
TL;DR: In this paper, a new proof of convergence of Adomian's method is presented, which is used for numerical applications to nonlinear integral equations, and series substition properties are used.