Stability Results for Discrete Volterra Equations: Numerical Experiments
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.
KeywordsRecurrence Relation Stability Criterion Volterra Integral Equation Linear Multistep Method Backward Differentiation Formula
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