Solving the Unstable Linear Fredholm Integral Equation of the First Kind by Means of a New Stochastic Algorithm
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A new "adsorption stochastic algorithm" (called ASA) is proposed for solving the unstable linear Fredholm integral equation of the first kind. The developed algorithm was applied for the calculation of the pore size distribution of activated carbons from single adsorption isotherms assuming different forms of the kernel (i.e. Dubinin and Radushkevich (DR) and/or Nguyen and Do (ND)) of a linear Fredholm integral equation of the first kind. The results obtained by ASA are compared with obtained applying, developed by Provencher, the advanced regularization CONTIN algorithm, advanced evolutionary algorithm GABI written by Arabas and modified by Kowalczyk, and simple evolutionary algorithm based on the mutation strategy labeled SASA. Additionally, the ASA results obtained by solving the integral equation with the ND kernel are compared with the results obtained by regularization solution of the integral equation with density functional theory (DFT) local isotherms as a kernel. It is shown that the developed ASA algorithm always provides stable and very similar results to the Tikhonov regularization method. Moreover, the ASA computations obtained for the ND local isotherms as a kernel are very similar to the results obtained by the most sophisticated regularization DFT software.