Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations — mentioned by ChrisRackauckas

Tue, 16 Sep 2025 18:11:39 GMT

B-S is just a (bad) explicit Runge-Kutta method. You can see this formally since if you take any order of the B-S method, you can write out its computation as a Runge-Kutta tableau. If you do this, you'll see it ends up being an explict RK method that has much higher f evaluations to achieve the leading truncation error coefficients and order that the leading RK methods get. For example, 9th order B-S uses IIRC about 2-3 times as many f evaluations as Vern9, while Vern9 gets like 3 orders of magnitude less error (on average w.r.t. LTE measurements). If you're curious about details of…

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Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations · HackerPapers discussions

Parallelizing Explicit and Implicit Extrapolation Methods for Ordinary Differential Equations — mentioned by ChrisRackauckas