Extrapolated Multirate Methods for Differential Equations with Multiple Time Scales

Authors:
Emil M. Constantinescu;Adrian Sandu
Affiliations:
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, USA 60439;Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, USA 24061
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

In this paper we construct extrapolated multirate discretization methods that allows one to efficiently solve problems that have components with different dynamics. This approach is suited for the time integration of multiscale ordinary and partial differential equations and provides highly accurate discretizations. We analyze the linear stability properties of the multirate explicit and linearly implicit extrapolated methods. Numerical results with multiscale ODEs illustrate the theoretical findings.