Recovery of the desorption activation energy distribution from the experimental temperature programmed desorption (TPD) spectra is among the most difficult problems of adsorption science. Since the heterogeneity effects strongly influence on transport, diffusion, and catalytic reaction time, the estimation of their magnitude is very important for practical purposes. Up to the present, several theories have been used for the interpretation of the TPD results. Almost all advanced theoretical approaches take into account the effect of surface disorder (heterogeneity in desorption activation energy); however, they ignore the numerical difficulties coming from the "ill-posed" character of the linear Fredholm integral equations appearing in the theoretical description of the TPD results. Thus, there is a growing interest in developing novel methods supported by powerful numerical algorithms taking this into account. In the current study we propose a new approach and consider the theoretical aspect as well as numerical problems appearing in the TPD analysis. Our modeling is based on the well-known and generally accepted "absolute rate theory," which has been used extensively for the interpretation of TPD results. We propose and verify (applying computer simulations) the new advanced numerical hybrid type algorithms taking into account the heterogeneity effects. They seem to be very promising in TPD spectra analysis. The stability of the proposed advanced numerical methods is confirmed by the computer simulation experiments, and the results are compared with those obtained from the condensation approximation (CA) method. (c) 2005 Elsevier Inc. All rights reserved.