An efficient approximate numerical method based on the principle of orthogonal collocation is presented for the computation of steady-state and transient active-ion concentration profiles in electrolyzers with axial dispersion. NOMENCLATURE collocation matrix [equation (A.4)] Tafel (intersection) parameters electrode area per unit length collocation matrix [equation (A.S)] Tafel (slope) parameters active ion concentration; c, its value at the electrode surface; c, its inlet value axial dispersion coefficient Faraday's constant electrolyte mass flow rate electrode separation distance grid size in a finite-difference algorithm mass balance parameter mass transport coefficient length of the electrodes (electrolyzer) orthogonal (shifted Legendre) polynomial Peclet number (VL/Di) concentration polarization coefficient the residual at collocation point x, cross sectional area of the electrolyzer dimensionless axial coordinate imposed voltage decomposition voltage mean linear electrolyte velocity regression parameters for the I-factor concentration parameter [equation (2)]: Xits value by regression electrolyte conductivity dimensionless time (product of mass flow rate and time divided by the mass of electrolyte in the electrolyzer)