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Heterogeneous multiscale methods for stiff ordinary differential equations

Authors: Bjorn Engquist and Yen-Hsi Tsai
Journal: Math. Comp. 74 (2005), 1707-1742
MSC (2000): Primary 65Lxx, 65Pxx, 37Mxx
Published electronically: May 18, 2005
MathSciNet review: 2164093
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Abstract: 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

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
Article copyright: © Copyright 2005 American Mathematical Society