# Stability Results for Discrete Volterra Equations: Numerical Experiments

• P. J. van der Houwen
• J. G. Blom
Part of the International Series of Numerical Mathematics book series (ISNM, volume 73)

## Abstract

In this paper we formulate a local stability criterion for linear multistep discretizations of first- and second-kind Volterra integral equations with finitely decomposable kernel. In a large number of numerical experiments this criterion is tested. We did not find examples which behaved unstable while the stability criterion predicted stability. However, we found several examples which behaved stable while the stability criterion predicted instability. A possible explanation may be the fact that the stability criterion is independent of the decomposition of the kernel, that is, it holds for the most ill-conditioned decomposition and consequently it may be rather pessimistic.

## Keywords

Recurrence Relation Stability Criterion Volterra Integral Equation Linear Multistep Method Backward Differentiation Formula
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