Partitioned rational Runge Kutta for parabolic systems

Wing Kam Liu*, Ted Belytschko, Yi Fei Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A new family of coupled time integration operators of different orders is developed. It permits different time integration operators to be used simultaneously in various regions of the model. This approach has the advantage of applying a very accurate time integrator, such as Runge Kutta method of order two to four, to the local nonlinear region of interest and a simple time integrator, such as the implicit–explicit or mixed time implicit–explicit method of order one, for the remaining region. The computer implementation aspects, stability analysis as well as the numerical evaluations of these new methods are presented. This is another attractive addition to the repertoire of time integration methods.

Original languageEnglish (US)
Pages (from-to)1581-1597
Number of pages17
JournalInternational Journal for Numerical Methods in Engineering
Issue number9
StatePublished - Sep 1984

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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