Numerical Methods and Exposure-Response

  • Douglas J. Crawford-Brown


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.


Order Rate Constant Integration Interval Geometric Standard Deviation Trapezoidal Method Transfer Rate Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Crawford-Brown, Theoretical and Mathematical Foundations of Human Health Risk Analysis, Kluwer Academic Publishers, Boston, 1997.CrossRefGoogle Scholar
  2. 2.
    Environmental Protection Agency, Exposure Factors Handbook, Office of Research and Development, Washington, DC, 1996.Google Scholar
  3. 3.
    I. Sokolnikoflf and R. Redheffer, Mathematics of Physics and Modern Engineering, McGraw-Hill, Inc., New York, 1966.Google Scholar
  4. 4.
    W. Press, B. Flannery, S. Teukolsky and W. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, University of Cambridge, Cambridge, England, 1988.Google Scholar
  5. 5.
    R. Hamming, Numerical Methods for Scientists and Engineers, Dover Publishers, New York, 1987.Google Scholar
  6. 6.
    C. Gerald and P. Wheatley, Applied Numerical Analysis, Addison-Wesley Publishing Co., Reading, Mass., 1998.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Douglas J. Crawford-Brown
    • 1
  1. 1.University of North CarolinaChapel HillUSA

Personalised recommendations