The two-dimensional Saul'yev method of simulating processes at a disk electrode is tested in the presence of homogeneous chemical reactions. The catalytic EC' reaction can produce a thin reaction layer, which is a test of any simulation method. The second-order Birk/Perone (B/P) reaction is similarly a test because of the nonlinear term appearing in the kinetic equations (although it does not give rise to a thin reaction layer). The Saul'yev method handles these with no special problems and is competitive, in terms of speed, with implicit methods at similar accuracy (and faster in the case of the nonlinear B/P case). (C) 2018 Elsevier Ltd. All rights reserved.