AbstractWe present the formulation, implementation, and performance evaluation of the Fourier pseudo‐spectral method for performing fast and accurate simulations of electrophoresis. We demonstrate the applicability of this method for simulating a wide variety of electrophoretic processes such as capillary zone electrophoresis, transient‐isotachophoresis, field amplified sample stacking, and oscillating electrolytes. Through these simulations, we show that the Fourier pseudo‐spectral method yields accurate and stable solutions on coarser computational grids compared with other nondissipative spatial discretization schemes. Moreover, due to the use of coarser grids, the Fourier pseudo‐spectral method requires lower computational time to achieve the same degree of accuracy. We have demonstrated the application of the Fourier pseudo‐spectral method for simulating realistic electrophoresis problems with current densities as high as 5000 A/m2 with over tenfold speed‐up compared to the commonly used second‐order central difference scheme, to achieve a given degree of accuracy. The Fourier pseudo‐spectral method is also suitable for simulating electrophoretic processes involving a large number of concentration gradients, which render the adaptive grid‐refinement techniques ineffective. We have integrated the numerical scheme in a new electrophoresis simulator named SPYCE, which we offer to the community as open‐source code.