  This study introduces new time-stepping strategies with built-in global error
estimators. The new methods propagate the defect along with the numerical
solution much like solving for the correction or Zadunaisky's procedure;
however, the proposed approach allows for overlapped internal computations and,
therefore, represents a generalization of the classical numerical schemes for
solving differential equations with global error estimation. The resulting
algorithms can be effectively represented as general linear methods. We present
a few explicit self-starting schemes akin to Runge-Kutta methods with global
error estimation and illustrate the theoretical considerations on several
examples.
