Runge-Kutta Starters for Multistep Methods

C. W. Gear

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


Runge-Kutta-like formulas which enable a multmtep method to start or restart at a high order after lust one Runge-Kutta (RK) step are presented. These formulas greatly improve the efficiency of mnltistep methods in a situation m which they were previously out performed by RK methodsi e., m which there are problems with frequent dlscontinmties or sudden large increases in derivatives, all of which cause an automatic program to reduce order and step size suddenly.

Original languageEnglish (US)
Pages (from-to)263-279
Number of pages17
JournalACM Transactions on Mathematical Software (TOMS)
Issue number3
StatePublished - Sep 1 1980

All Science Journal Classification (ASJC) codes

  • Software
  • Applied Mathematics


  • Runge-Kutta
  • integration
  • mnltistep
  • ordinary dfferential equations


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