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Superconvergent explicit two-step peer methods

✍ Scribed by Rüdiger Weiner; Bernhard A. Schmitt; Helmut Podhaisky; Stefan Jebens

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 817 KB
Volume: 223
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.02.014

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✦ Synopsis

We consider explicit two-step peer methods for the solution of nonstiff differential systems. By an additional condition a subclass of optimally zero-stable methods is identified that is superconvergent of order p = s + 1, where s is the number of stages. The new condition allows us to reduce the number of coefficients in a numerical search for good methods. We present methods with 4-7 stages which are tested in FORTRAN90 and compared with DOPRI5 and DOP853. The results confirm the high potential of the new class of methods.

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