Exploration Of Precise Integration Implicit Algorithm About The Nonlinear Dynamics

Molecular Dynamics is a popular subject in recent years, many practical problems can use Molecular Dynamics to simulate the experiment, the precise integration methods to accelerate the process of molecular dynamics, rich in Molecular Dynamics in the practical problems’solution. With the continuous application of the precise integration methods, in recent years, many of new methods are created, the reason for the Molecular Dynamics began to tend to the precise integration of a variety of methods, because the precise time step integration methods can be more accurately numerical solution, and avoid the matrix inversion, and improve the results are more stable, more efficient.This article studies the method of solution of nonlinear problems in Molecular Dynamics, the time integration applications based on the precise integration of new implicit algorithm. First, a brief introduction to the traditional sense of the nonlinear dynamic problems and to address issues related to special methods and direct method of calculation. Then, combined with molecular dynamics, derived equations for the time implicit scheme. The method is the separation of the linear part and nonlinear part of the nonlinear equations, the equations homogeneous part of the application of traditional precise integration algorithm, because it points out of the index matrix iteration step refinable approximation, to avoid the matrix inverse solution of the homogeneous equations can be obtained directly, non-homogeneous equations, the implicit method, in order to avoid the iterative method, directly using a simple iterative or center difference quotient approximation derivative. Finally, the specific nonlinear delay dynamic equation examples and the hard-sphere collision model example of a conservative system as well as the external interference system to the new algorithm efficiency and accuracy, and stability analysis.