The Automatic Integration of Ordinary Differential Equations

C. W. Gear

Research output: Contribution to journalArticlepeer-review

559 Scopus citations


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.

Original languageAmerican English
Pages (from-to)176-179
Number of pages4
JournalCommunications of the ACM
Issue number3
StatePublished - Mar 1 1971

ASJC Scopus subject areas

  • General Computer Science


  • differential equations
  • integration
  • order control
  • step control
  • stiff equations


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