Abstract
This paper is concerned with Lax-Wendroff methods for a class of hyperbolic history value problems. These problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the Lax-Wendroff method for smooth solutions and investigate numerically the dependence on the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term).