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 + ∝0t (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.
|Original language||English (US)|
|Number of pages||14|
|Journal||Journal of Mathematical Analysis and Applications|
|State||Published - May 1 1986|
ASJC Scopus subject areas
- Applied Mathematics