The ordinary successive approximations method and Padé approximants for solving a differential equation with variant retarded argument
type: Item
instance of: scholarly article
title: The ordinary successive approximations method and Padé approximants for solving a differential equation with variant retarded argument
zbMATH Open document ID: 1030.65083
DOI: 10.1016/S0096-3003(02)00424-1
author: Ercan Çelik
author: Arzu Aykut
author: Mustafa Bayram
published in: Applied Mathematics and Computation
publication date: 2003-08-07T00:00:00Z
review text: The authors present a numerical method to solve boundary value problems for differential equations with retarded argument. At first they derive a Fredholm-Volterra integral equation which is equivalent to the original differential problem. Then the existence and uniqueness of solution is proved together with convergence of successive approximations, defined by a Green function. At last, it is shown that the use of Padé series provides numerical stability. An interesting example is numerically solved, to support the previoulsy presented theoretical results.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 1961566
zbMATH Keywords: differential equations with retarded arguments
zbMATH Keywords: numerical examples
zbMATH Keywords: boundary value problems
zbMATH Keywords: Fredholm-Volterra integral equation
zbMATH Keywords: convergence
zbMATH Keywords: successive approximations
zbMATH Keywords: Green function
zbMATH Keywords: Padé series
zbMATH Keywords: numerical stability
Wikidata QID: Q115339749
reviewed by: Raffaella Pavani
MaRDI profile type: Publication
cites work: Q5642900
cites work: Q3994364
cites work: Analytical approximations and Padé approximants for Volterra's population model
cites work: The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation
cites work: Arbitrary order numerical method for solving differential-algebraic equation by Padé series
full work available at URL: s0096-3003(02)00424-1
OpenAlex ID: W2139332915
description: scientific article; zbMATH DE number 1961566