 Improved accuracy for time-splitting methods for the numerical solution of parabolic equationsA. Arrarás and L. Portero Applied Mathematics and Computation, 2015, vol. 267, issue C, 294-303 Abstract: In this work, we study time-splitting strategies for the numerical approximation of evolutionary reaction–diffusion problems. In particular, we formulate a family of domain decomposition splitting methods that overcomes some typical limitations of classical alternating direction implicit (ADI) schemes. The splitting error associated with such methods is observed to be O(τ2) in the time step τ. In order to decrease the size of this splitting error to O(τ3), we add a correction term to the right-hand side of the original formulation. This procedure is based on the improved initialization technique proposed by Douglas and Kim in the framework of ADI methods. The resulting non-iterative schemes reduce the global system to a collection of uncoupled subdomain problems that can be solved in parallel. Computational results comparing the newly derived algorithms with the Crank–Nicolson scheme and certain ADI methods are presented. Keywords: Alternating direction implicit; Domain decomposition; Partition of unity; Splitting error; Time-splitting method (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:267:y:2015:i:c:p:294-303 DOI: 10.1016/j.amc.2015.03.073 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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