The time discretization in classes of integro-differential equations with completely monotonic kernels: weighted asymptotic stability
type: Item
instance of: scholarly article
title: The time discretization in classes of integro-differential equations with completely monotonic kernels: weighted asymptotic stability
zbMATH Open document ID: 1266.65212
author: Da Xu
published in: Science China. Mathematics
publication date: 2013-04-08T00:00:00Z
review text: The paper is devoted to a study of the behaviour of a numerical method when used to discretize certain linear convolution type integro-differential equations whose kernels are linear combinations of finitely many completely monotonic functions with coefficients \(\geq 1\). The numerical scheme is a backward Euler method combined with a first-order convolution quadrature for the memory term. The main emphasis of the paper is on providing sufficient conditions for the numerical method to be asymptotically stable in a weighted norm on \((0, \infty)\).
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45K05
zbMATH DE Number: 6151452
zbMATH Keywords: time discretization
zbMATH Keywords: completely monotonic kernel
zbMATH Keywords: backward Euler method
zbMATH Keywords: convolution quadrature
zbMATH Keywords: weighted \(l ^{1}\) asymptotic stability
zbMATH Keywords: linear convolution type integro-differential equations
MaRDI profile type: Publication
full work available at URL: s11425-012-4410-2
OpenAlex ID: W2267904245
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DOI: 10.1007/S11425-012-4410-2
description: scientific article; zbMATH DE number 6151452