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We study the relationship between local and global error in Runge-Kuttamethods for initial-value problems in ordinary differential equations. We showthat local error control by means of local extrapolation does not equate toglobal error control. Our analysis shows that the global error of thehigher-order solution is propagated under iteration, and this can cause anuncontrolled increase in the global error of the lower-order solution. We findconditions under which global error control occurs during the initial stages ofthe RK integration, but even in such a case the global error is likely toeventually exceed the user-defined tolerance.

Runge-Kutta Methods: Local error control does not imply global error control