A symplectic approach for boundary-value problems of linear hamiltonian systems

A symplectic approach based on canonical transformation and generating functions was proposed to solve boundary-value problems of linear Hamiltonian systems. According to the relationship between the generating function and the state-transition matrix, an interval merge recursive algorithm was constructed to calculate the coefficient matrices of the 2nd-type genera-ting function for linear homogeneous Hamiltonian systems, which was further extended to non-homogeneous cases. Then the properties of the generating function were used to transform the boundary-value problems to initial-value problems. Finally, the general initial-value problems were solved with the symplectic numerical method to preserve the geometric structure of the Hamiltonian system. Numerical simulations show the validity of the presented approach for linear homogeneous and nonhomogeneous problems, and the advantages of the symplectic numerical method to preserve the intrinsic properties of Hamiltonian systems.