Abstract
A class of quasilinear parabolic Volterra integrodifferential equations, which includes models for the stretching of filaments of molten polymers, is solved numerically. Due to the presence of small parameters and large relaxation constants, an implicit Euler type discretization scheme is chosen. A convergence proof for sufficiently small solutions is given, which also shows that the scheme preserves the asymptotic character of the solutions of the continuous problem as t → ± ∞. Computations are reported, which focus on a comparison of the solutions in cases where inertial, Newtonian and viscoelastic effects have various relative importance.