Adsorption integral equation via complex approximation with
constraints: the Langmuir kernel
Abstract
The relationship between the measured adsorption isotherm and
unknown energy distribution function is described by so-called
adsorption integral equation, a linear Fredholm integral
equation of the first kind. We consider the case of the
Langmuir kernel when the equation can be reduced to the
Stieltjes integral equation. A new method for solving the
Stieltjes equation is developed. The method is based on the
ideas of complex approximation with constraints. The numerical
algorithms constructed on the base of this method allow to
reduce the problem under consideration to linear or
linear-quadratic programming problems. The method is compared
with the usual regularization methods. The obtained results can
be useful for the evaluation of the experimental adsorption
energy distribution from experimental data.