Solving Ordinary Differential Equations with Discontinuities

C. W. Gear, O. Osterby

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


Automatic codes for differential equations can be inadequate when the solutions have discontinuities. If the user provides an external mdicator for discontinuities (e.g., a switching function whose sign changes Indicate discontinuities), a code can be more efficient. Atechnique for detection and location of a discontinuity IS discussed which can be implemented when such indicators are not practical. It estimates the order and magmtude of the discontinuity and hence the stepsize which keeps the error under control while stepping over the discontinuity.

Original languageEnglish (US)
Pages (from-to)23-44
Number of pages22
JournalACM Transactions on Mathematical Software (TOMS)
Issue number1
StatePublished - Jan 1 1984

All Science Journal Classification (ASJC) codes

  • Software
  • Applied Mathematics


  • Multistep
  • differential equations
  • discontinuities
  • singularities


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