A new simulation algorithm is presented for describing the dynamics of diffusion reactions at the most common microelectrode 1D (planar, cylindrical, spherical) and 2D geometries (band, disk) for electrochemical mechanisms of any complexity and involving fast homogeneous reactions of any kind. A series of typical electrochemical mechanisms that create the most severe simulation difficulties is used to establish the exceptional performance and accuracy of this algorithm, which stem from the combination of (quasi)conformal transformation of space and a new method for auto-adaptive grid compression.