New results on the analytic summation of Adomian series for some classes of differential and integral equations
type: Item
instance of: scholarly article
title: New results on the analytic summation of Adomian series for some classes of differential and integral equations
zbMATH Open document ID: 1206.65175
author: I. L. El-Kalla
published in: Applied Mathematics and Computation
publication date: 2011-01-14T00:00:00Z
review text: Using the Adomian decomposition, the author obtains the solution of a linear first order initial value problem of an ordinary differential equation in the form of an infinite series of terms composed by the successive integration by parts. Parallely, he obtains the closed form of an infinite number of successive integrations by parts and, then, he identifies the previous solution with this closed form. The same closed form solution was early obtained by an integral factor technique. The above closed form can be used to obtain closed form solutions for non-linear higher order initial value problems for initial-boundery value problems and for a class of Volterra-type integral equations.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 5836667
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: Volterra-type integral equations
zbMATH Keywords: Adomian decomposition method
zbMATH Keywords: linear first order
zbMATH Keywords: initial value problem
zbMATH Keywords: infinite series
zbMATH Keywords: integration by parts
zbMATH Keywords: non-linear higher order
MaRDI profile type: Publication
full work available at URL: j.amc.2010.09.034
OpenAlex ID: W1991157901
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DOI: 10.1016/J.AMC.2010.09.034
description: scientific article; zbMATH DE number 5836667