Superconvergent explicit two-step peer methods

Authors:
Rüdiger Weiner;Bernhard A. Schmitt;Helmut Podhaisky;Stefan Jebens
Affiliations:
Institut für Mathematik, Universität Halle, D-06099 Halle, Germany;Fachbereich Mathematik und Informatik, Universität Marburg, D-35032 Marburg, Germany;Institut für Mathematik, Universität Halle, D-06099 Halle, Germany;Institut für Troposphärenforschung Leipzig, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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.