The locally adaptive choise of time step in molecular dynamics' problems

This paper considers numerical methods in molecular dynamics. An overview of the existing methods and algorithms is made. A necessary condition for convergence of an arbitrary finite-difference scheme, which solves newtonian differential equations of motion is formulated and proved. From bounding the scheme energy source in the two-body problem, a criteria for choosing time step is deduced. Based on this criteria, an original algorithm of the N-body problem numerical integration is constructed. All the modern ways of constructing new schemes are unifyed in that algorithm. On the example of two model problems it is shown, that the proposed algorithm guarantees both the control of energy fluctuations and the significant calculation acceleration.