Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China
Abstract:
The present paper deals with the stability properties of numerical methods for Volterra integral equations with delay argument. We assess the numerical stability of numerical methods with respect to the following test equations(0.1a) $$y\left( t \right) = \psi \left( 0 \right) + \int_0^t {\left( {py\left( s \right) + q\left( {s - \tau } \right)} \right)ds (0 \leqslant t \leqslant X)}$$ (0.1b) $$y\left( t \right) = \psi \left( t \right) \left( {t \in - \tau ,0)} \right)$$ where τ is a positive constant, and P and q are complex valued. We investigate the stability properties of reducible quadrature methods and θ-methods in the case of the above test equations