C. W. Gear
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.
- 1 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.Google Scholar
- 2 Henrici, P. Discrete Variable Methods in Ordinary Differential Equations, Wiley, New York, 1962, Ch. 5.Google Scholar
- 3 Gear, C.W. The numerical integration of ordinary differential equations. Math. Comp. 21,2(Apr. 1967), 146-156.Google ScholarCross Ref
- 4 Nordsieck, A. On numerical integration ofordinary differential equations. Math. Comp. 16, 1 (Jan. 1962), 22-49.Google ScholarCross Ref
- 5 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.Google ScholarDigital Library
- 6 Morrison, D. Optimal mesh size in the numerical integration of an ordinary differential equation. J. A CM 9, 1 (Jan. 1962), Google ScholarDigital Library
Index Terms
- The automatic integration of ordinary differential equations
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