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 ABSTRACT
An integration technique for the automatic solution of an initial value problem for a set of ordinary differential equations is described. A criterion for the selection of the order of approximation is proposed. The objective of the criterion is to increase the step size so as to reduce solution time. An option permits the solution of “stiff” differential equations. A program embodying the techniques discussed appears in Algorithm 407.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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Gear, C.W. The automatic integration of stiff ordinary differential equations. Information Processing 68, A. J. H. Morrell, Ed., North Holland, Amsterdam, 1969, pp. 187-193.
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Henrici, P. Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962, Ch. 5.
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Gear, C.W. The numerical integration of ordinary differential equations. Math. Comp. 21,2(Apr. 1967), 146-156.
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Nordsieck, A. On numerical integration ofordinary differential equations. Math. Comp. 16, 1 (Jan. 1962), 22-49.
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Greenspan, H., Harrier, W., and Riberic, M. On varying step size in numerical integration of first order ordinary differential equations. Numer. Math. 7, (1965), 286-291.
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CITED BY 15
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D. L. Kalmey , D. S. Kerr , L. J. White, Numerical experimentation with routines for solving nonlinear systems of equations, Proceedings of the annual conference, p.438.1-439, August 27-29, 1973, Atlanta, Georgia, United States
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Gruia-Catalin Roman , David Garfinkel , Carl B. Marbach, Memory conserving efficient methods for solving large sets of stiff differential equations, Proceedings of the June 7-10, 1976, national computer conference and exposition, June 07-10, 1976, New York, New York
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