Towards solving the unstable linear Fredholm equation of the first kind-a new procedure called adsorption stochastic algorithm (ASA) and its propertiess

The paper consists of three main parts. In the first, a new "adsorption stochastic algorithm" (called ASA) for solving the unstable linear Fredholm integral equation of the first kind is proposed. In this program. some procedures of estimating the relative minimum in one dimension are tested. The newly developed algorithm is applied in the second part for reconstructing some pore size distribution functions (monomodal and multimodal). Moreover, the influence of a random noise on the stability of the solution of the inverse problem is studied. In the third part, the experimental verification of the above-mentioned method is presented. The results calculated by ASA are compared with those obtained by applying advanced regularization CONTIN and INTEG algorithms. It is shown that the developed ASA method always provides stable and very similar results to Tikhonov's regularization method. Moreover, the ASA computations obtained for the Nguyen and Do local isotherms as the kernel are very similar to the results calculated by the most sophisticated regularization density functional theory software. Summing up, the method can be very useful for evaluating the pore size distribution from experimental data.