Abstract
In this paper we prove that direct linear multistep methods for Volterra integral equations of the second kind with repetition factor equal to one are always stable. We show trivially that this result is not true for first kind equations. We also demonstrate constructively that direct linear multistep methods for both first and second kind Volterra integral equations can have repetition factors greater than one, and indeed of arbitrary high order, and be numerically stable. Finally we explain why the first form of Simpson's rule for second kind equations is stable while the second form is unstable.
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