Numerical solution of linear Volterra equations with partial integrals
type: Item
instance of: scholarly article
title: Numerical solution of linear Volterra equations with partial integrals
zbMATH Open document ID: 1334.65206
author: V. A. Kalitvin
published in: Journal of Mathematical Sciences (New York)
publication date: 2016-01-21T00:00:00Z
review text: The author generalizes the application of the Gauss quadrature method to approximately solve the second kind Volterra integral equation \[ x(t,s)=(Kx)(t,s)+ f(t,s), \] defined on the space \( C(D)\), \(D= [a,b]\times [c,d]\) of functions of two variables. The theorem proves the convergence of the quadrature method, imposing several conditions on the step size, the coefficients of the formula and others. The class of quadrature formulas that correspond to these assumptions is not specified.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 6534005
zbMATH Keywords: Volterra linear integral equation
zbMATH Keywords: quadrature method
zbMATH Keywords: convergence
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: s10958-015-2434-1
OpenAlex ID: W1000256312
cites work: Q4951124
cites work: On Volterra-Fredholm equations with partial integrals
cites work: Q5589673
DOI: 10.1007/S10958-015-2434-1
description: scientific article; zbMATH DE number 6534005