New symplectic five-stage schemes for molecular dynamics problems

Source abstract

We consider the Forest-Ruth family of symplectic vestage Runge-Kutta type schemes for the numerical solution of molecular dynamics problems described by systems with a separable Hamiltonian. A twostep optimization method for nding symplectic schemes of high order of accuracy is proposed. In fact, a method has been proposed for increasing the accuracy of symplectic di erence schemes with a xed number of stages by obtaining real schemes with the smallest norm of the leading term of the di erence scheme approximation error. 146 new vestage schemes of the fourth order of accuracy were found using numerical optimization. A comparison was made of the stability conditions of the Forest-Ruth schemes with a number of stages of 3, 4, and 5. The accuracy of the new schemes was demonstrated using the example of a numerical solution to the Kepler twobody problem. It is shown that the new vestage schemes provide higher accuracy of particle energy conservation than the best known fourstage fourth-order schemes and the wellknown second-order Verlet scheme.