In the solution of estuary pollution problems, the mathematical model is a partial differential equation, which is often replaced by a set of ordinary differential equations with time as the independent variable. The solution to these equations is taken as the solution of the partial differential equations at points dx apart. A significant problem is to determine the closeness of the solution of the ordinary differential equation to the solution of the partial differential equation, the spacing dx, and the number of sections. The closeness of the solution can be judged by examining the magnitude and phase of the frequency response of the partial differential equations and the set of ordinary differential equations. Selecting a given phase error allows one to obtain a relation giving the allowed spacing dx. Selecting an attenuation error sets the number of sections. Thus, from the knowledge of the frequency response of the system the rules developed give the number of sections and spacing to meet specified errors in the approximation. (Key words: Computers, digital; estuaries; frequency analysis; pollution; quality of water)