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arXiv · 2311.11581

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

Sergio Blanes·Fernando Casas·Luke Shaw
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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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Sergio Blanes, Fernando Casas, Luke Shaw. 2023-11-20. Generalized extrapolation methods based on compositions of a basic 2nd-order scheme. https://arxiv.org/abs/2311.11581

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