Kyungpook Mathematical Journal 2015; 55(2): 301-311
Published online June 23, 2015
Copyright © Kyungpook Mathematical Journal.
Error Control Strategy in Error Correction Methods
Philsu Kim and Sunyoung Bu
Department of Mathematics, Kyungpook National University, Daegu 702-701, Korea
In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al.~cite{kim2011a,kim2011b}. We formulate the local truncation error at each time and calculate the approximated solution using the solution and the formulated truncation error at previous time for achieving uniform error bound which enables a long time simulation. Numerical results show that the error controlled ECM provides a clue to have uniform error bound for well conditioned problems~cite{Atkinson89}.
Keywords: Error Correction Method, Runge-Kutta method, Error control, Local truncation error, Well-conditioned problem