sentences: New expressions for one-sided finite-difference approximations are proposed. In these approximations the odd-order error terms are eliminated while the even-order terms are left to be taken care of by Richardson extrapolation. The effective local truncation error is shown to be less than for higher-order one-sided finite-difference approximations but the solutions for a test problem are shown to have comparable accuracy for both approximations. 2006 Elsevier Inc. All rights reserved.