Generating Function Methods For Coefficient-varying Generalized Hamiltonian Systems

Structure-preserving algorithms for Hamiltonian systems in the unremittingefforts of scientists have been fruitful. In regard to Hamiltonian systems on Pois-son manifolds, the research into the generating function method has been done forseveral special cases only. At ?rst, this paper brie?y introduces the symplectic-structure-preserving algorithms for classical Hamiltonian systems and Poisson-structure-preserving algorithms for generalized Hamiltonian systems with con-stant coe?cients. Then, based on the results of the generating function methodfor generalized Hamiltonian systems with constant coe?cients, this paper con-structs the generating functions for coe?cient-varying generalized Hamiltoniansystems, gets a kind of Poisson-structure-preserving algorithms for solving thisclass of systems. And the method is applied to solve the dynamical systemswhich can be written into generalized Hamiltonian form (such as generalizedLotka-Volterra systems, Robbins equations and so on). At last, this paper givesthe corresponding numerical experiments to analyse this kind of algorithms.