Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: J. S. C. PRENTICE
Pages: [71] - [84]
Received Date: August 31, 2011
Submitted by:
We study the relationship between local and global errors 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.
Runge-Kutta, local error, global error, local extrapolation.
