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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Heterogeneous multiscale methods for stiff ordinary differential equations
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by Bjorn Engquist and Yen-Hsi Tsai PDF
Math. Comp. 74 (2005), 1707-1742 Request permission


The heterogeneous multiscale methods (HMM) is a general framework for the numerical approximation of multiscale problems. It is here developed for ordinary differential equations containing different time scales. Stability and convergence results for the proposed HMM methods are presented together with numerical tests. The analysis covers some existing methods and the new algorithms that are based on higher-order estimates of the effective force by kernels satisfying certain moment conditions and regularity properties. These new methods have superior computational complexity compared to traditional methods for stiff problems with oscillatory solutions.
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Additional Information
  • Bjorn Engquist
  • Affiliation: Department of Mathematics and PACM, Princeton University, Princeton, New Jersey 08544, and Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden
  • MR Author ID: 63590
  • Yen-Hsi Tsai
  • Affiliation: Institute for Advanced Study and Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 731088
  • Email:
  • Received by editor(s): July 31, 2003
  • Received by editor(s) in revised form: June 4, 2004
  • Published electronically: May 18, 2005
  • Additional Notes: The second author is partially supported by the National Science Foundation under agreement No. DMS-0111298
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1707-1742
  • MSC (2000): Primary 65Lxx, 65Pxx, 37Mxx
  • DOI:
  • MathSciNet review: 2164093