COLLAPSIBLE BACKWARD CONTINUATION AND NUMERICAL APPROXIMATIONS IN A FUNCTIONAL-DIFFERENTIAL EQUATION

The phenomenon of a wild kind of oscillatory behavior found in solutio ns of the scalar differential equation with scaling on time, (x) over dot (t) = -ax(t) + ax(pt), is investigated in this paper. It is shown that this phenomenon does not, in general, reflect a similar behavior in this equation's numerical solutions. The results obtained here may be extended, under appropriate assumptions, to other types of nonlinea r multidimensional retarded functional differential equations with van ishing delays. (C) 1998 Academic Press.