High-order Runge–Kutta–Nyström geometric methods with processing Original Research Article

We present new families of sixth- and eighth-order Runge–Kutta–Nyström geometric integrators with processing for ordinary differential equations. Both the processor and the kernel are composed of explicitly computable flows associated with non trivial elements belonging to the Lie algebra involved in the problem. Their efficiency is found to be superior to other previously known algorithms of equivalent order, in some case up to four orders of magnitude.