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Generalized extrapolation methods based on compositions of a basic 2nd-order scheme

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  • Blanes, S.
  • Casas, F.
  • Shaw, L.

Abstract

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization of extrapolation methods and multi-product expansions. A general analysis is provided and new methods up to order 8 are built and tested. The new approach is shown to reduce the latency problem when implemented in a parallel environment and leads to schemes that are significantly more efficient than standard extrapolation when the linear combination is delayed by a number of steps.

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  • Blanes, S. & Casas, F. & Shaw, L., 2024. "Generalized extrapolation methods based on compositions of a basic 2nd-order scheme," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    • Handle: RePEc:eee:apmaco:v:473:y:2024:i:c:s0096300324001358
    DOI: 10.1016/j.amc.2024.128663
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