An easy-to-use variant of the finite difference method (FDM), the polynomial finite difference method (PFDM), for the numerical solution of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs), is presented. Compared to the traditional implementation of the FDM, the PFDM approach has two major advantages: straightforward implementation, and easily adjustable accuracy order. Some examples are presented to compare the numerical solutions of the PFDM to those of other popular ODEs/DAEs; methods. These examples show that the PFDM also has the following good features: feasible for ODEs/DAEs in the implicit form, capable of self-starting in high orders, and applicable to stiff problems. (C) 2003 Elsevier Ltd. All rights reserved.