#splittingmethods — Public Fediverse posts
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I am excited to see "Splitting methods for differential equations" by Sergio Blanes, Fernando Casas and Ander Murua on arXiv: https://arxiv.org/abs/2401.01722
This is a review article to be published in the excellent Acta Numerica. It discusses numerical methods for solving differential equations which can be split in several parts that are easier to solve. In formulas, the (ordinary or partial) differential equation is 𝑑𝑢/𝑑𝑡 = 𝑓(𝑢) and the splitting is 𝑓(𝑢) = 𝑓₁(𝑢) + 𝑓₂(𝑢).
For people that don't do numerical analysis or computational mathematics, it may be helpful to think of the Lie–Trotter product formula
\[ e^{A+B} = \lim_{n\to\infty} (e^{A/n}e^{B/n})^n. \]
This is the simplest splitting method. Part of the game is to find formulas that converge faster.