Volume preservation of Butcher series methods from the operadic viewpoint

Abstract: After a quick introduction on Butcher series methods, we recall the theorem of Iserles-Quispel-Tse/Chartier-Murua on the nonexistence of volume preserving Butcher series methods. We will then give some algebraic and combinatorial recollections on operads, and introduce the operads and the techniques appearing in the new proof of this theorem. If time permits, we will explain how the operadic viewpoint also allows us to recover the full classification of volume preserving aromatic Butcher series methods, which was first computed by Laurent, McLachlan, Munthe-Kaas, and Verdier.

commutative algebraclassical analysis and ODEsnumerical analysisrings and algebras

Audience: researchers in the topic

( chat | paper | video )

Algebraic and Combinatorial Perspectives in the Mathematical Sciences

Series comments: To receive announcements: Register into our mailing list by going to our main website www.math.ntnu.no/acpms/