The time evolutions of the kinetic (δE_kin,i,δE_kin,e) and field (δE_fld,i,δE_fld,e) energies of ions and electrons as well as the total energy (δE_total) in decaying turbulence simulations, where given initial turbulent fields decay. (a) In the conventional model for computing passing electrons (Δt∼0.005 μs), the accumulation of errors in the electron energy owing to high-frequency noise violates energy conservation, whereas (b) in the new hybrid kinetic-electron model (Δt∼0.02 μs), the time-step width is extended (lower computational cost) and the accuracy of energy conservation is improved by eliminating high-frequency noise.