Sinc approximation for numerical solution of integral equation arising in conductor-like screening model for real solvent

Abstract

In this study, we present the existence of solutions for some nonlinear integral equations known as Hammerstein type which forms the basis for the conductor-like screening model for real solvents (COSMO-RS). By using the techniques of noncompactness measures, we employ the basic fixed point theorems such as Darbo’s theorem to obtain the mentioned aim in Banach algebra. Then this paper presents a powerful numerical approach based on the Sinc approximation to solve the equation which forms the basis for the conductor-like screening model for real solvents (COSMO-RS). The approach is based on the recognition of the Hammerstein integral equation for the determination of the chemical potential of a surface segment as a function of screening charge density. Then convergence of this technique is discussed by preparing a theorem which shows an exponential type convergence rate and guarantees the applicability of that.