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Recently, the class of energy-conserving Runge-Kutta methods namedHamiltonian Boundary Value Methods (HBVMs), has been proposed for the efficientsolution of Hamiltonian problems, as well as for other types of conservativeproblems. In this paper, we report further advances concerning such methods,resulting in their enhanced version (Enhanced HBVMs, or EHBVMs). The basictheoretical results are sketched, along with a few numerical tests on aHamiltonian problem, taken from the literature, possessing multiple invariants.

Enhanced HBVMs for the numerical solution of Hamiltonian problems with multiple invariants