AbstractThe reduction‐to‐periodicity method using the pseudospectral fast Fourier transform (FFT) technique is applied to the solution of non‐periodic problems, including the two‐dimensional incompressible Navier–Stokes equations. The accuracy of the method is explored by calculating the derivatives of given functions, one‐ and two‐dimensional convective‐diffusive problems, and by comparing the relative errors due to the FFT method with a second‐order finite difference (FD) method. Finally, the two‐dimensional Navier–Stokes equations are solved by a fractional step procedure using both the FFT and the FD methods for the driven cavity flow and the backward‐facing step problems. Comparisons of these solutions provide a realistic asses