Abstract
We study the difference equations obtained when some numerical methods for Volterra integral equations of the second kind are applied to the linear test problem y( t) = 1 + ∝ 0 t ( λ + μt + vs) y( s) ds, t ⩾ 0, with fixed stepsize h. The resulting difference equations are of Poincaré type and we formulate a criterion for boundedness of solutions of these equations if the associated characteristic polynomial is a simple von Neumann polynomial. This result is then used in stability analysis of reducible quadrature methods for Volterra integral equations.
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