Skip to main content

Numerical integration aspects of a nutrient utilization ecological problem

Part of the Lecture Notes in Mathematics book series (LNM,volume 362)

Keywords

  • Extrapolation Scheme
  • Variable Stepsize
  • NASA Marshall Space
  • Local Error Tolerance
  • Scientific Subroutine Package

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Canale, R.P., Frazho, D.B., and Powers, W.F., "Application of Optimal Control Theory in Modeling Nutrient Utilization and Phytoplankton Production in Lakes", University of Michigan, Report AC-101, February 1973

    Google Scholar 

  2. Chen, C.W., "Concepts and Utilities of Ecologic Model", Journal of the Sanitary Engineering Division, Proceedings of the American Society of Civil Engineers, Vol. 96, No. SA5, October 1970

    Google Scholar 

  3. Riley, G.A., "Theory of Food-Chain Relations in the Ocean", page 438–463 in Hill, M.N. (editor) The Sea, 2, Interscience, New York, 1963

    Google Scholar 

  4. Canale, R.P., "A Methodology for Mathematical Modeling of Biological Production", Report to the University of Michigan Sea Grant, 1970

    Google Scholar 

  5. DiToro, D.M., O'Connor, D.J., and Thomann, R.V., "A Dynamic Model of the Phytoplankton Population in the Sacramento-San Joaquin Delta", Nonequilibrium Systems in Natural Water Chemistry, Advances in Chemistry Series 106, 1971

    Google Scholar 

  6. IBM System/360, Scientific Subroutine Package, (360A-CM-03X) Version III (1968) IBM Technical Publication Department, DRKGS subroutine

    Google Scholar 

  7. Fehlberg, E., "Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas with Stepsize Control", NASA TR R-287, October 1968

    Google Scholar 

  8. Schwausch, O.A., "A Fortran Subroutine for the Numerical Integration of First Order Ordinary Differential Equations Using Either a Fixed or Variable Integration Step Size", Personal Communication, Lockheed Electronics Company, Houston, Texas, 1968

    Google Scholar 

  9. Krogh, F.T., "VODQ/SVDQ/DVDQ — Variable Order Integrators for the Numerical Solution of Ordinary Differential Equations", TU Document No. CP-2308, NPO-11643, JPL, Pasadena, Calif., May 1969

    Google Scholar 

  10. Bulirsch, R. and Stoer, J., "Numerical Treatment of Ordinary Differential Equations by Extrapolation Methods", Num. Math, Vol. 8, 1966, pp. 1–13

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Gear, C.W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, 1971

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1974 Springer-Verlag

About this paper

Cite this paper

Frazho, D.B., Powers, W.F., Canale, R.P. (1974). Numerical integration aspects of a nutrient utilization ecological problem. In: Bettis, D.G. (eds) Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations. Lecture Notes in Mathematics, vol 362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066591

Download citation

  • DOI: https://doi.org/10.1007/BFb0066591

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06602-6

  • Online ISBN: 978-3-540-37911-9

  • eBook Packages: Springer Book Archive