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The numerical solution of systems of stiff ordinary differential equations

Published online by Cambridge University Press:  24 October 2008

J. R. Cash
J. R. Cash
Affiliation:
Department of Mathematics, Imperial College, London, S.W. 7
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Abstract

Algorithms are developed for the numerical solution of systems of first-order ordinary differential equations, the solutions of which have widely different rates of variation. The iterative procedures described use a step length of integration proportional to the rate of change of the required slowly varying solution in a region of integration, where either the transient components of the complete solution have become negligible compared with the chosen working accuracy or in a region where rapidly increasing components of the solution are theoretically possible but are made absent by the initial conditions. Several numerical examples are given to demonstrate the algorithms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 443 - 456
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Barton, D., Willers, I. M. and Zahar, R. V. M.Mathematical software. Ed. Rice, J. (Academic Press, 1971).Google Scholar
(2)Barton, D., Willers, I. M. and Zahar, R. V. M.The automatic solution of systems of ordinary differential equations by the method of Taylor Series. Comput. J. 14 (1971), 243–248.CrossRefGoogle Scholar
(3)Brayton, R., Gustavson, F. and Liniger, W.A numerical analysis of the transient behaviour of a transistor circuit. IBM J. Res. Develop. 10 (1966), 292–299.CrossRefGoogle Scholar
(4)Cash, J. R.The numerical solution of linear stiff differential equations. Proc. Cambridge Philos. Soc. 71 (1272), 505–515.CrossRefGoogle Scholar
(5)Dahlquist, G. G.A special stability criterion for linear multistep methods. BIT, 3 (1963), 22–43.CrossRefGoogle Scholar
(6)Emanuel, G. Problems underlying the numerical integration of the chemical and vibrational rate equations in a near-equilibrium flow. AFDC-TDR-63–82, Aerospace Corp., El Segundo, (1963).CrossRefGoogle Scholar
(7)Fox, L.The numerical solution of ordinary and partial differential equations (Pergamon Press, 1962).Google Scholar
(8)Gear, C. W.Numerical initial value problems in ordinary differential equations (Prentice-Hall, 1971).Google Scholar
(9)Lapidus, L. and Seinfeld, J. H.The numerical solution of ordinary differential equation (Academic Press, 1971).Google Scholar
(10)Robertson, H.Numerical analysis —an introduction. Ed. Walsh, J. (Academic Press, 1964), pp. 178–182.Google Scholar