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SIAM J. Sci. Comput. 31, pp. 4452-4477 (26 pages)
Extrapolated Implicit-Explicit Time Stepping
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Add to FacebookThis paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method-of-lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, easy to implement, and straightforward to parallelize. This work establishes the existence of perturbed asymptotic expansions of global errors, explains the convergence orders of these methods, and studies their linear stability properties. Numerical results with stiff ODE, DAE, and PDE test problems confirm the theoretical findings and illustrate the potential of these methods to solve multiphysics multiscale problems.
© 2010 Society for Industrial and Applied Mathematics
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Received August 14, 2008
Accepted November 02, 2009
Published online January 15, 2010
Accepted November 02, 2009
Published online January 15, 2010
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