We describe several numerical methods developed to analyze the behavior of spin polarized liquids in the presence of long-range magnetic dipolar interactions and external field gradients. Two of the methods use a discrete lattice of spins. In the first we calculate the magnetic field from the lattice of. spins directly, either in the rotating frame; or in the lab frame. In the second method, we include the dipolar, fields from linear magnetization gradients analytically and calculate the dipolar fields from higher order gradients in Fourier space, where they area local function of the magnetization. In the third method the magnetization is expanded in a Taylor series and the dipolar fields are calculated analytically for each term. The results of these calculations are compared to experimental data, in which we use two superconducting quantum interference device magnetometers, adjacent to a spherical sample of hyperpolarized liquid Xe-129 to detect the evolution of magnetization gradients. In particular, we observe an increase by a factor of 100 of the spin dephasing time in a longitudinal magnetic field gradient due to dipolar interactions of the spins. While each of the numerical techniques has certain limitations, they are generally in agreement with each other and with experimental data. (C) 2004 American Institute of Physics.