Error Control Strategy in Error Correction Methods

Abstract

In this paper, we present the error control techniques for the error correction methods (ECM) which is recently developed by P. Kim et al.[8, 9] 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 [1]