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.
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