Parallelism across time in ODEs

C. W. Gear, Xu Xuhai

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


There is no natural parallelism across time in ODEs, so to exploit massive parallelism for a small system of equations it is necessary to use iterative techniques in time, such as waveform. The Picard method, for example, allows each integration to be performed in O(log N) time over N time steps but its convergence is poor for any but almost quadrature problems (∂f∂y small). Generalized Picard, or waveform, may have much faster convergence but less parallelism. This paper considers parallelism across time, explores a proposal made in an earlier paper [2], and reports on some tests made on that method.

Original languageEnglish (US)
Pages (from-to)45-68
Number of pages24
JournalApplied Numerical Mathematics
Issue number1-3
StatePublished - Jan 1993

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


  • Differential equations
  • initial value problems


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