Collapsible Backward Continuation and Numerical Approximations in a Functional Differential Equation

The phenomenon of a wild kind of oscillatory behavior found in solutions of the scalar differential equation with scaling on time,x(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 equationʹs numerical solutions. The results obtained here may be extended, under appropriate assumptions, to other types of nonlinear multidimensional retarded functional differential equations with vanishing delays.