Legendre collocation method and its convergence analysis for the numerical solutions of the conductor-like screening model for real solvents integral equation

In this paper, a reliable algorithm for solving the nonlinear Hammerstein integral equation arising from chemical phenomenon is presented. The conductor-like screening model for real solvents (COSMO-RS) 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. Also, this method is using a simple computational manner and its error analysis will be discussed by illustrating some theorems. Finally, two numerical experiments are given to confirm the superiority and efficiency of presented method with respect to some other well-known methods such as the Bernstein collocation method, Haar wavelet method and Sinc collocation method.