Lepton number and energy conservation (see Equations (27) and (28), respectively) in relaxation problems with high (left column) and low (right column) collision rates. Each plot shows the relative changes in lepton number and energy in the relaxation simulations with the nonlinear solver tolerance tol set to 10⁻⁸ (black solid line) and 10⁻¹² (black dashed line). Tightening the tolerance from 10⁻⁸ to 10⁻¹² leads to approximately 4 orders of magnitude smaller relative changes in both lepton number and energy.