Skip to main content

Solving odes in quasi steady state

  • 550 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 968)

Abstract

Solving ordinary differential equations (ODEs) with solutions in a quasi steady state has been studied by computational chemists, applied mathematicians, and numerical analysts. Because of this, it is a very appropriate topic for this interdisciplinary workshop.

In this paper we shall first discuss what stiffness is for model problems arising in chemical kinetics. Chemists and applied mathematicians have made use of quasi steady state approximations (singular perturbation theory) to alter the problem so as to avoid stiffness. The approach is described and some difficulties noted. Numerical analysts have developed methods to solve general stiff ODEs. How they relate to the problem at hand is described and some difficulties pointed out. Finally, ideas from both approaches are combined. The new combination deals effectively with stiffness when the quasi steady state hypothesis is valid.

Keywords

  • Quasi Steady State
  • Singular Perturbation Theory
  • Stiff Problem
  • Forward Euler Method
  • Quasi Steady State Approximation

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. Edsberg, L., Integration package for chemical kinetics, in R. A. Willoughby, ed., Stiff Differential Systems, Plenum Press, New York, 1974.

    Google Scholar 

  2. Clark, R. L. and G. F. Groner, A CSMP/360 precompiler for kinetic chemical equations, Simulation, 19(1972) 127–132.

    CrossRef  Google Scholar 

  3. Robertson, H. H., Numerical integration of systems of stiff ordinary differential differential equations with special structure, in G. Hall and J. M. Watt, eds., Modern Numerical Methods for Ordinary Differential Equations, Clarendon Press, Oxford, 1976.

    Google Scholar 

  4. Villadsen, J., and M. L. Michelsen, Solution of Differential Equation Models by Polynomial Approximation, Prentice-Hall, Englewood Cliffs, NJ, 1978.

    MATH  Google Scholar 

  5. Bjurel, G., et al., Survey of stiff ordinary differential equations, Rept. NA 70.11, Dept. Inf. Proc. Comp. Sci., Royal Inst. Tech., Stockholm, 1970.

    Google Scholar 

  6. Young, T. R., and J. P. Boris, A numerical technique for solving stiff ordinary differential equations associated with the chemical kinetics of reactive-flow problems, J. Phys. Chem., 81 (1977) 2424–2427.

    CrossRef  Google Scholar 

  7. Young, T. R., CHEMEQ — a subroutine for solving stiff ordinary differential equations, Rept. NRL 4091, Naval Res. Lab., Washington, D.C., 1980.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Shampine, L.F. (1982). Solving odes in quasi steady state. In: Hinze, J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064891

Download citation

  • DOI: https://doi.org/10.1007/BFb0064891

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11970-8

  • Online ISBN: 978-3-540-39374-0

  • eBook Packages: Springer Book Archive