Iterative Solution of the Ornstein-zernike Equation with Various Closures Using Vector Extrapolation
نویسندگان
چکیده
The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the xed point iterations is relatively slow. We consider transformations of the sequence of solution vectors using non-linear sequence transformations, so-called vector extrapolation processes. An example is the vector J transformation. The transformed vector sequences turn out to converge considerably faster than the original sequences. In this paper we investigate acceleration methods for solving the fundamental equation for the pair distribution function of classical many-particle systems , the so-called Ornstein-Zernike equation. The thermodynamic properties of such systems are determined by the interaction between the particles from which the system is built up. If one knows the two-particle distribution function g, one can calculate all thermodynamic properties of the considered system. g is deened in the canonical ensemble by 1, Chapter 4]
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