Palindromic 3-stage splitting integrators, a roadmap
For computational scientists using splitting integrators, the paper offers practical improvements over the widely used Strang/Verlet method with minimal implementation overhead.
The paper studies palindromic 3-stage splitting integrators, showing they can be easily implemented like the Strang/Verlet method and identifying parameter choices that outperform it, including a fourth-order effective method for PDEs and perturbations improving efficiency in molecular dynamics and Hybrid Monte Carlo.
The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the Strang/Verlet integrator. We study in detail the two-parameter family of palindromic, three-stage splitting formulas and identify choices of parameters that may outperform the Strang/Verlet method. One of these choices leads to a method of effective order four suitable to integrate in time some partial differential equations. Other choices may be seen as perturbations of the Strang method that increase efficiency in molecular dynamics simulations and in Hybrid Monte Carlo sampling.