A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations
type: Item
instance of: scholarly article
title: A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations
zbMATH Open document ID: 1252.65211
DOI: 10.1590/S1807-03022012000100010
author: R. Katani
author: Sedaghat Shahmorad
published in: Computational and Applied Mathematics
publication date: 2012-08-08T00:00:00Z
full work available at URL: http://www.scielo.br/scielo.php
review text: An efficient block by block numerical methods is proposed in order to solve systems of linear and nonlinear first and second kind Volterra integral equations of Urysohn type. The method is based on the Romberg quadrature rule which involves the trapezoidal or the Simpson quadrature formula and eventually can use the Lagrange interpolation. Due to its simplicity, the method can be easily implemented for an increasing number of blocks and for obtaining better accuracy. The convergence of the method is proved and the order of convergence is at least six. The performances of the method are illustrated on four numerical examples in comparison with the homotopy perturbation method and a modification of the radial basis function network method. Three examples are devoted to second kind integral equations and in another example to integral equations of the first kind. The block by block method is shown to be more effective. The numerical results are obtained by programming in Maple 11.
reviewed by: Alexandru Mihai Bica
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 6064104
zbMATH Keywords: Urysohn type Volterra integral equations
zbMATH Keywords: Romberg quadrature rule
zbMATH Keywords: block by block method
zbMATH Keywords: nonlinear systems
zbMATH Keywords: Simpson quadrature formula
zbMATH Keywords: Lagrange interpolation
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: homotopy perturbation method
zbMATH Keywords: radial basis function network method
describes a project that uses: Maple
MaRDI profile type: Publication
OpenAlex ID: W2002858760
description: scientific article; zbMATH DE number 6064104