The adaptive moving-grid strategy suggested in Parts 1-3 for the solution of electrochemical kinetic partial differential equations in one space dimension has been subject to further evaluation and tuning. The strategy has been applied to two kinetic examples of fast homogeneous reaction-diffusion systems involving extremely thin moving reaction zones away from the electrodes. One example, the simulation of the double-potential step transient for a simple mechanism of electrogenerated chemiluminescence, has been considered in much detail. As the second example the simulation of the linear potential scan voltammetry for a double-electron transfer with "nuances" has been briefly discussed. The adaptive grid strategy provides effective, satisfactorily accurate and complete solutions to these difficult problems, which would not be possible to obtain by traditional fixed-grid finite difference methods, except at much higher computational cost or with radical simplifications.