I have read a lot about numerical integrators (ode solvers) lately and tried reading a few papers but I have stumbled upon something that I can't understand and it's something called ABA and BAB.

For example in this paper New families of symplectic splitting methods for numerical integration in dynamical astronomy they have tables with coefficients but I haven't figured out how to interpret those and code an algorithm with them because I haven't found what ABA and BAB schemes are, Google isn't helping me a lot sadly. How are those tables meant to be interpreted?

  • $\begingroup$ It looks like they are introduced in equation 5. It seems they define sampling points relative to the timestep size for a splitting of the solution (indexed by a and b)? $\endgroup$
    – Emil
    Commented Mar 21, 2019 at 22:48
  • $\begingroup$ Seems like there was a lot more to it than I thought 😅. Do you know anywhere I could read up on those things? $\endgroup$ Commented Mar 22, 2019 at 8:16

1 Answer 1


You may want to check out Section 3 in chapter III of:

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration: structure-preserving algorithms for ordinary differential equations, Second., vol. 31. Berlin: Springer-Verlag, 2006.


A. Murua, “The Hopf Algebra of Rooted Trees, Free Lie Algebras, and Lie Series,” Foundations of Computational Mathematics, vol. 6, no. 4, pp. 387–426, Nov. 2006.


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