Numerical methods for Volterra equations of the second kind
type: Item
instance of: scholarly article
title: Numerical methods for Volterra equations of the second kind
zbMATH Open document ID: 0575.65139
DOI: 10.1007/BF02575910
author: Giuseppe Piazza
published in: Calcolo
publication date: 1984-01-01T00:00:00Z
review text: The author studies the stability and the order of two numerical methods for the integration of the Volterra equation \(f(x)=g(x)+\int^{x}_{x_ 0}K(x,y,f(y))dy\), \(x\in [x_ 0,X]\). These methods are based on the integration, by using the trapezoidal rule or a backward differentiation type formula, of the differential equations system derived formally by differentiating m-times (m\(\geq 2)\) the given Volterra equation. Numerical examples are given.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 3919760
zbMATH Keywords: quadrature formula method
zbMATH Keywords: stability
zbMATH Keywords: order
zbMATH Keywords: Volterra equation
zbMATH Keywords: backward differentiation
zbMATH Keywords: Numerical examples
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
cites work: Stability Regions in the Numerical Treatment of Volterra Integral Equations
cites work: Q5674335
cites work: Backward differentiation type formulas for Volterra integral equations of the second kind
cites work: Numerical solution of Volterra integral equation
cites work: Q5629991
cites work: Q3863013
description: scientific article; zbMATH DE number 3919760