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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Edsberg, L., Integration package for chemical kinetics, in R. A. Willoughby, ed., Stiff Differential Systems, Plenum Press, New York, 1974.
Clark, R. L. and G. F. Groner, A CSMP/360 precompiler for kinetic chemical equations, Simulation, 19(1972) 127–132.
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.
Villadsen, J., and M. L. Michelsen, Solution of Differential Equation Models by Polynomial Approximation, Prentice-Hall, Englewood Cliffs, NJ, 1978.
Bjurel, G., et al., Survey of stiff ordinary differential equations, Rept. NA 70.11, Dept. Inf. Proc. Comp. Sci., Royal Inst. Tech., Stockholm, 1970.
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.
Young, T. R., CHEMEQ — a subroutine for solving stiff ordinary differential equations, Rept. NRL 4091, Naval Res. Lab., Washington, D.C., 1980.
Author information
Authors and Affiliations
Editor information
Rights 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