Title: On the convergence and local splitting error of different splitting schemes

Authors: Istvan Farago, Agnes Havasi

Addresses: Department of Applied Analysis, Eotvos Lorand University, Pazmany P. setany 1/C, H-1117 Budapest, Hungary. ' Department of Applied Analysis, Eotvos Lorand University, Pazmany P. setany 1/C, H-1117 Budapest, Hungary

Abstract: The convergence of different splitting methods – sequential, Strang, weighted sequential and weighted Strang splitting – is investigated in the semigroup context both for linear and m-dissipative operators, by use of the Trotter product formula and Lax|s equivalence theorem. The local splitting errors of the Strang and weighted Strang schemes are analysed with the help of the Baker-Campbell-Hausdorff formula. It is shown that both methods, generally of second order, can be higher than second-order accurate if certain conditions are met. Our results are illustrated with examples.

Keywords: Strang splitting; CFD; computational fluid dynamics; convergence; semigroup; local splitting error; shallow water model; sequential splitting; operator splitting.

DOI: 10.1504/PCFD.2005.007684

Progress in Computational Fluid Dynamics, An International Journal, 2005 Vol.5 No.8, pp.495 - 504

Published online: 01 Sep 2005 *

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