Numerical Solution of a Singularly Perturbed Nonlinear Volterra Equation.

摘要

The paper describes a numerical solution of a problem which arises in polymer rheology. A mathematical model was derived to describe the elastic recovery of molten plastics. This model is replaced by a discrete model, for which the solution can immediately be constructed by computer. The main part of this paper concerns the relation between the solutions to the original and discretized models. The original problem is a Volterra equation; Volterra equations usually occur when one models evolutions which depend on their history. We would like to emphasize that when one solves Volterra equations numerically, it is important that the discrete problem have similar qualitative properties to the original one. In the particular problem considered here, this forces us to choose a rather poorly convergent method if we wish to guarantee the results obtained. The numerical results confirm a discrepancy between theory and experiments indicated previously, namely that when the elongation of a filament is large and rapid, the model predicts somewhat more recovery than is observed experimentally.