Methods of investigation numerical simulation of the relaxation of a macromolecular ensemble in a viscoelastic medium

A numerical dynamic model is examined of the ensemble of polymer molecules in a viscoelastic medium. The molecules are chains of spherical elements joined by elastic forces. The motion of elements is described by the generalized Langevin equation which allows for the frictional force against the medium with a delay determined by the nucleus of friction and the Gaussian random force with correlation properties satisfying the fluctuation-dissipation theorem. Numerical methods are proposed for solving the generalized Langevin equation with an arbitrary memory function. Results are given of numerical experiments of simulating the dynamics of the ensemble of 103 molecules, consisting of two, three and nine elements. In the simplest case of unidimensional motion of the chain formed of two elements joined by elastic force, in viscoelastic medium, results of numerical calculation agree with analytical control solutions of the problem.