Numerical Algorithm for the Order Verification of Numerical Methods Sayfy S. Khoury sayfy@aus.edu skhoury@aus.edu Abstract In this paper, we have introduced a unified approach for the order verification of the errors in Taylor polynomial approximations and many numerical methods. An algorithm, based on the computer algebra system "MAPLE, is written and tested by verifying the error for many familiar numerical methods that arise in the undergraduate curriculum, such as, Taylor polynomial approximation, Newton's method for solving equations, the 5-point forward numerical differentiation formula, the composite Simpson rule, the 4-stage explicit Runge-Kutta method, and the 3-point Gaussian integration formula. The algorithm offers a simple and unified way to understand and verify the error of Taylor approximations as well as numerical methods. Thus it is convenient for teaching purposes in the undergraduate mathematics curriculum.