Numerical Methods and Exposure-Response

Abstract

Catenary systems of compartments, in which flow of a pollutant is in one direction through a chain of compartments and where the rates of movement are controlled by first-order kinetics, can be described by differential equations with analytic solutions regardless of the number of compartments (see Chapter 3). Even if flow is in several directions, analytic solutions may be found for some relatively simple cases (see Chapter 4). As the complexity of the system increases, however, with large numbers of mutually connected compartments, the ability to produce analytic solutions to the underlying differential equations increases greatly. Even if analytic solutions can be found in principle, they may involve such long derivations as to make the task impractical.