Discretization with variable time steps of an evolution equation with a positive-type memory term
type: Item
instance of: scholarly article
title: Discretization with variable time steps of an evolution equation with a positive-type memory term
zbMATH Open document ID: 0858.65143
DOI: 10.1016/0377-0427(95)00025-9
published in: Journal of Computational and Applied Mathematics
publication date: 1997-03-11T00:00:00Z
review text: The authors consider the problem \[ u'(t) + \int^t_0 \beta (t-s) Au(s)ds = f(t) \quad \text{for} \quad t>0,\;u(0)=v. \] Here \(A\) is a selfadjoint positive definite operator in a real Hilbert space \(H\), and \(\beta\) is a real-valued positive definite kernel. The equation is discretized in time using backward Euler and Crank-Nicolson methods, and incorporating appropriate quadratures for the memory term (integral term). Variable time steps are permitted. Error estimates of the methods are derived.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 47G20
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 908402
zbMATH Keywords: evolution equations
zbMATH Keywords: backward Euler methods
zbMATH Keywords: finite difference method
zbMATH Keywords: abstract Volterra integral equation
zbMATH Keywords: variable time steps
zbMATH Keywords: error estimates
zbMATH Keywords: selfadjoint positive definite operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: Crank-Nicolson methods
zbMATH Keywords: memory term
author: William Mclean
author: Vidar Thomée
author: L. B. Wahlbin
reviewed by: G. Vainikko
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00025-9
OpenAlex ID: W1972645181
cites work: Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
cites work: Time discretization of parabolic problems by the discontinuous Galerkin method
cites work: Numerical solution of an evolution equation with a positive-type memory term
cites work: Positive quadratures for Volterra equations
description: scientific article; zbMATH DE number 908402