Abstract
In this paper we present a simple, general methodology for the generation of high-order operator decomposition (“splitting”) techniques for the solution of time-dependent problems arising in ordinary and partial differential equations. The new approach exploits operator integration factors to reduce multiple-operator equations to an associated series of single-operator initial-value subproblems. Two illustrations of the procedure are presented: the first, a second-order method in time applied to velocity-pressure decoupling in the incompressible Stokes problem; the second, a third-order method in time applied to convection-Stokes decoupling in the incompressible Navier-Stokes equations. Critical open questions are briefly described.
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Maday, Y., Patera, A.T. & Rønquist, E.M. An Operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow. J Sci Comput 5, 263–292 (1990). https://doi.org/10.1007/BF01063118
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DOI: https://doi.org/10.1007/BF01063118