  In a previous paper, a technique was suggested to avoid order reduction with
any explicit exponential Runge-Kutta method when integrating initial boundary
value nonlinear problems with time-dependent boundary conditions. In this
paper, we significantly simplify the full discretization formulas to be applied
under conditions which are nearly always satisfied in practice. Not only a
simpler linear combination of $\varphi_j$-functions is given for both the
stages and the solution, but also the information required on the boundary is
so much simplified that, in order to get local order three, it is no longer
necessary to resort to numerical differentiation in space. The technique is
then shown to be computationally competitive against other widely used methods
with high enough stiff order through the standard method of lines.
