  The renormalization-group equation (RGE) approach to neutrino matter effects
is further developed in this work. We derive a complete set of differential
equations for effective mixing elements, masses and Jarlskog-like invariants in
presence of a light sterile neutrino. The evolutions of mixing elements as well
as Jarlskog-like invariants are obtained by numerically solving these
differential equations. We calculate terrestrial matter effects in
long-baseline (LBL) experiments, taking NOvA, T2K and DUNE as examples. In both
three-flavor and four-flavor frameworks, electron-neutrino survival
probabilities as well as the day-night asymmetry of solar neutrino are also
evaluated as a further examination of the RGE approach.
