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The automatic integration of ordinary differential equations

By C. W. Gear
Communications of the ACM, March 1971, Vol. 14 No. 3, Pages 176-179
10.1145/362566.362571
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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.

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