Global error analysis of the Chebyshev rational approximation method

Olin Calvin, Sebastian Schunert, Barry Ganapol

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM's accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. We show that the reason for CRAM's behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.

Original languageEnglish (US)
Article number107828
JournalAnnals of Nuclear Energy
StatePublished - Jan 2021


  • Chebyshev rational approximation method
  • Doubling method
  • Nuclear depletion
  • Rattlesnake code

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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