Stability of reducible quadrature methods for Volterra integral equations of the second kind
type: Item
instance of: scholarly article
title: Stability of reducible quadrature methods for Volterra integral equations of the second kind
zbMATH Open document ID: 0573.65104
DOI: 10.1007/BF01389707
author: V. L. Bakke
author: Zdzislaw Jackiewicz
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133029
review text: Based on the test equation \[ y(t)=1+\int^{t}_{0}(\lambda +\mu t+\nu s)y(s)ds \] a stability analysis of reducible quadrature methods for second kind Volterra integral equations is presented. Since the above integral equation is equivalent to a second order differential equation (with non-constant coefficients), the numerical solution satisfies a finite recurrence relation. The boundedness of the analytical solution of the differential equation as well as that of the numerical solution of the recurrence relation are investigated. The results are then illustrated for the \(\theta\)-method. The importance of the above test equation is still not clear, since in applications usually the kernel is bounded or converges to zero when t-s\(\to \infty\).
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 3915591
zbMATH Keywords: theta method
zbMATH Keywords: reducible quadrature methods
zbMATH Keywords: second kind
zbMATH Keywords: finite recurrence relation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3915591