  This paper presents a sequence of deferred correction (DC) schemes built
recursively from the implicit midpoint scheme for the numerical solution of
general first order ordinary differential equations (ODEs). It is proven that
each scheme is A-stable, satisfies a B-convergence property, and that the
correction on a scheme DC(2j) of order 2j of accuracy leads to a scheme DC2j+2
of order 2j+2. The order of accuracy is guaranteed by a deferred correction
condition. Numerical experiments with standard stiff and non-stiff ODEs are
performed with the DC2, ..., DC10 schemes. The results show a high accuracy of
the method. The theoretical orders of accuracy are achieved together with a
satisfactory stability.
