Palindromic 3-stage splitting integrators, a roadmap

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.MSS has been supported by projects MTM2013-46553-C3-1-P from Ministerio de Economía y Comercio, and MTM2016-77660-P (AEI/FEDER, UE) from Ministerio de Economía, Industria y Competitividad, Spain. CMC was supported by Junta de Castilla y León, Spain, together with the European Social Fund through a postdoctoral position held at the Instituto de Matemáticas de la Universidad de Vallolid, IMUVA