Strongly stable one-step methods for stiff Volterra integral equations of the second kind
type: Item
instance of: scholarly article
title: Strongly stable one-step methods for stiff Volterra integral equations of the second kind
zbMATH Open document ID: 0633.65138
DOI: 10.1007/BF02576531
author: B. George
published in: Calcolo
publication date: 1986-01-01T00:00:00Z
review text: We propose some implicit methods for stiff Volterra integral equations of the second kind. The methods are constructed on the integro-differential equation obtained by differentiation of the Volterra equation. The numerical schemes are derived using a class of A-stable and L-stable methods for ordinary differential equations associated with the Gregory quadrature formula. Related to the test equation: \(y(t)=1+\int^{t}_{0}[\lambda +\mu (t-s)]y(s)ds\), \(\lambda,\mu <0\) we give the definition of \({\mathcal A}\)-stability and \({\mathcal L}\)-stability for the proposed numerical methods as natural extension of the A-stability and L-stability for the schemes for solving ordinary differential equations. We show how to choose the parameters of the methods in order to obtain \({\mathcal A}\)-stable and \({\mathcal L}\)-stable schemes. Because of these properties the proposed schemes are particularly advantageous in the case of stiff Volterra integral equations.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 4030935
zbMATH Keywords: one-step methods
zbMATH Keywords: implicit methods
zbMATH Keywords: stiff Volterra integral equations of the second kind
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: \(A\)-stable methods
zbMATH Keywords: \(L\)-stability
MaRDI profile type: Publication
cites work: Q4151113
cites work: Implicit Runge-Kutta methods for second kind Volterra integral equations
cites work: Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
cites work: Numerical methods for Volterra equations of the second kind
cites work: Backward differentiation type formulas for Volterra integral equations of the second kind
description: scientific article; zbMATH DE number 4030935