  We report on a novel algorithm for controlling global error in a step-by-step
(stepwise) sense, in the numerical solution of a scalar, autonomous, nonstiff
or weakly stiff problem. The algorithm exploits the remainder term of a Taylor
expansion of the solution. It requires the use of the DP853 triple to solve an
auxiliary problem which, in turn, enables the remainder term to be determined.
A quenching process then allows the solution generated by Euler's method to be
controlled. We have achieved tolerances on the relative global error as strict
as 1e-10.
