Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

Olin W. Calvin, Barry D. Ganapol, R. A. Borrelli

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

Original languageEnglish (US)
Pages (from-to)558-588
Number of pages31
JournalNuclear Science and Engineering
Issue number4
StatePublished - 2023
Externally publishedYes


  • Adding and Doubling Method
  • Bateman equation
  • Chebyshev Rational Approximation Method
  • depletion

ASJC Scopus subject areas

  • Nuclear Energy and Engineering


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