Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9511607 | Applied Numerical Mathematics | 2005 | 14 Pages |
Abstract
A class of implicit two-step integration methods is introduced having s stages which may be computed in parallel. Since all stage solutions are approximations with equal accuracy and stability properties these methods were attributed as 'peer' methods. Using a special result on Vandermonde matrices we identify one subclass of order sâ1 which is zero stable for general stepsize sequences. A further analysis for singularly perturbed problems shows that no order reduction occurs and the accuracy is essentially determined by the regularity of the smooth component. These results are backed by several numerical examples even including one differential algebraic problem.
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Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
B.A. Schmitt, R. Weiner, K. Erdmann,