Convergence and asymptotic error expansion for Euler's method for variable delay differential equations (Q2489718)

In spite of the fact that the author never published his doctoral dissertation titled ``Discretization methods for retarded ordinary differential equations'' (UCLA, 1964), his work became a guide for many researchers in the field of numerical methods for delay differential equations. Now, one of them, Zdzislaw Jackiewicz, presents selected portions of that dissertation, choosing those results that have proven over the years to have been the most useful to numerical analysts. After defining the initial value problem for a retarded ordinary differential equation, the author presents several variations of a first-order one-step method for approximating the solution. Convergence is studied in details. This unusual paper is remarkable from both numerical and historical point of view.