Fourier spectral and pseudospectral methods are used in numerical modeling of ionospheric processes, namely macroscopic evolution of naturally and artificially created ionospheric density irregularities. The simulation model consists of two-dimensional electrostatic nonlinear fluid plasma equations that describe the plasma evolution. The spectral and pseudospectral methods are used to solve the spatial dependence of these self-consistent equations. They are chosen over the widely used finite difference and finite element techniques since spectral methods are straightforward to implement on nonlinear equations. They are at least as accurate as finite difference simulations. A potential equation solver is developed to solve the nonlinear potential equation iteratively. Time integration is accomplished using a combination of leapfrog and leapfrog-trapezoidal methods. A FORTRAN program is developed to implement the simulation model. All calculations are performed in the Fourier domain. The simulation model is tested by considering three types of problems. This is accomplished by specifying an initial density (Pedersen conductivity) profile that represents slab model density, density enhancement (due to releases such as barium), or density depletion (due to late times effects of electron attachment material releases) in the presence of a neutral wind. The evolution of the irregularities is monitored and discussed. The simulation results agree with similar results obtained using finite difference methods. A comparison is made between the ionospheric depletion and enhancement problems. Our results show that, given the same parameters and perturbation level, the depletion profiles bifurcate much faster than that of the enhancement. We argue that this is due to the larger growth rate in the E X B interchange instability of the density depletion case. / Master of Science