An efficient method based on the Legendre polynomials for the numerical solutions of conductor-like screening model for real solvents integral equation

. In this paper, an efficient algorithm for solving the conductor-like screening model for real solvents (COSMO-RS) integral equation is presented. Firstly, COSMO-RS integral equation will be converted to the nonlinear Hammerstein integral equation. Then, the nonlinear Hammerstein integral equation will be solved by the shifted Legendre collocation method. This method approximates the unknown function with Legendre polynomials. The merits of this algorithm lie in the fact that, on the one hand, the problem will be reduced to a nonlinear system of algebraic equations. On the other hand, we show that the efficiency and accuracy of the shifted Legendre collocation method for solving these equations are remarkable. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Finally, a numerical experiment is given to confirm the superiority and efficiency of presented method with respect to some other well-known methods.