A Laplace decomposition algorithm applied to a class of nonlinear differential equations
type: Item
instance of: scholarly article
title: A Laplace decomposition algorithm applied to a class of nonlinear differential equations
zbMATH Open document ID: 0996.65068
DOI: 10.1155/S1110757X01000183
published in: Journal of Applied Mathematics
publication date: 2001-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/49479
review text: Using Laplace transform, the author constructs recursively an approximate solution of an initial value problem of the nonlinear differential equation \[ y''+ a(x)y'+ b(x) y= f(y), \] where the nonlinear term \(f(y)\) is decomposed in terms of Adomian polynomials [see \textit{G. Adomian}, Solving frontier problems of physics: The decomposition method, Kluwer, Dordrecht (1994; Zbl 0802.65122)]. But the convergence of this method is not considered. Some numerical examples are given, where higher iterates of the approximate solution are computed by a computer algebra system.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1749295
zbMATH Keywords: decomposition method
zbMATH Keywords: Laplace transform
zbMATH Keywords: initial value problem
zbMATH Keywords: nonlinear differential equation
zbMATH Keywords: Adomian polynomials
zbMATH Keywords: numerical examples
author: S. A. Khuri
describes a project that uses: Maple
MaRDI profile type: Publication
OpenAlex ID: W1967539618
description: scientific article; zbMATH DE number 1749295