The inverse problem in electroencephalography (EEG) consists of localizing the sources within the brain that produce the scalp-measured potentials. The present study investigates various algorithms designed for providing a reliable solution to the inverse problem, focusing on specific sleep EEG waveforms called spindles. Firstly, an analytical model was used, the head being simulated as a piecewise homogeneous conductor consisting of four concentric spheres. As a second step, a numerical solution was evaluated, using the Finite Volume Method (FVM). Performance evaluation was carried on using simulated current sources and various additive Gaussian noise levels. Performance was better for superficial sources. The simulations indicated that both algorithms could perform the reconstruction of the underlying brain electrical activity accurately, even if noise was raised to a fairly high level (SNR=20 dB). Application of the methods to real sleep EEG data provided sleep spindle sources at the thalamus, the parietal and the central area of the cerebral cortex in accordance with existing literature.