Improvement of methods for molecular dynamics integration

An application of symplectic implicit Runge-Kutta (RK) integration schemes, the s-stage Gauss-Legendre Runge-Kutta (GLRK) methods of order 2s, for the numerical solution of molecular dynamics (MD) equation is described, The two-stage fourth-order GLRK method, the implicit midpoint rule, and the three-stage diagonally implicit RK method of order four are studied. The fixed-point iteration was used for solving the resulting nonlinear system of equations. The algorithms were applied to a complex system of N particles interacting through a Lennard-Jones potential. The proposed symplectic methods for MD integration permit a wide range of time steps, are highly accurate and stable, and are thus suitable for the MD integration