  We study the relationship between local and global error in Runge-Kutta
methods for initial-value problems in ordinary differential equations. We show
that local error control by means of local extrapolation does not equate to
global error control. Our analysis shows that the global error of the
higher-order solution is propagated under iteration, and this can cause an
uncontrolled increase in the global error of the lower-order solution. We find
conditions under which global error control occurs during the initial stages of
the RK integration, but even in such a case the global error is likely to
eventually exceed the user-defined tolerance.
