1. Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S Cass Avenue, Argonne, IL, 60439, USA 2. Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA
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.