High accuracy combination method for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind
type: Item
instance of: scholarly article
title: High accuracy combination method for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind
zbMATH Open document ID: 1192.65163
DOI: 10.1155/2010/901587
author: Lu Pan
author: Xiaoming He
author: Tao Lü
published in: Mathematical Problems in Engineering
publication date: 2010-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/231559
review text: Summary: This paper presents a high accuracy combination algorithm for solving systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of a combination algorithm, we can obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover, an a posteriori error estimation for the algorithm is derived. Both the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational cost.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 5728523
zbMATH Keywords: high accuracy combination algorithm
zbMATH Keywords: systems of nonlinear Volterra integral and integro-differential equations
zbMATH Keywords: weakly singular kernels
zbMATH Keywords: second kind
zbMATH Keywords: quadrature algorithms
zbMATH Keywords: a posteriori error estimation
zbMATH Keywords: numerical examples
Wikidata QID: Q58653404
MaRDI profile type: Publication
OpenAlex ID: W2046731378
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description: scientific article; zbMATH DE number 5728523