A natural regularization of the adsorption integral equation with Langmuir-kernel

Abstract

AbstractAdsorption integral equations are used to compute adsorption energy distributions by measured total isotherms. Since these types of equations are Fredholm integral equations of the first kind on bounded domains, they are unstable or ill-posed, respectively. Hence, there is a need for regularization. In this work, we present general regularizations based on the fourier transform for a special kernel, the Langmuir kernel. The regularization parameters are chosen as zeros or minimizers of simple functions depending on the mean absolute error of a transformed total isotherm. In difference to many other solutions proposed, an explicit error and convergence analysis is made. Additionally, we consider adsorption energy distributions with sharp peaks or for ideal adsorbents. Here, we construct a regularization for computing averages of the adsorption energy distribution and the maximal approximation error is estimated uniformly.