The use of very high order spatial discretisation in digital simulation of electrochemical experiments is assessed, considering up to asymmetric 8-point approximations for the derivatives. A wide range of conditions are examined, including several mechanisms and electrodes and potential-step and potential-sweep experiments. In all cases it is found that asymmetric multi-point approximations in combination with exponentially expanding grids provides very accurate results and with very reduced number of grid points (<15). Consequently, the direct ('brute force') resolution of the finite-difference equation system by standard matrix techniques becomes a competitive and more general alternative to specialised methods like the Thomas algorithm. (C) 2015 Elsevier B.V. All rights reserved.