Abstract
AbstractThe explicit symplectic difference schemes are considered for the numerical solution of molecular dynamics problems described by systems with separable Hamiltonians. A general method for finding symplectic schemes of high order of accuracy using parametric Gröbner bases, resultants, and permutations of variables is proposed. The implementation of the method is described by the example of four-stage partitioned Runge–Kutta (PRK) schemes of the Forest–Ruth family. All required symbolic calculations are performed using the computer algebra system Mathematica. 96 new PRK schemes of Forest–Ruth family have been obtained.KeywordsMolecular dynamicsSymplectic difference schemesPartitioned schemesGröbner basesResultantsPermutations
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