TY - JOUR
T1 - Quadratic Invariants and Symplectic Structure of General Linear Methods
AU - Xiao , Ai-Guo
AU - Li , Shou-Fu
AU - Yang , Min
JO - Journal of Computational Mathematics
VL - 3
SP - 269
EP - 280
PY - 2001
DA - 2001/06
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8979.html
KW - Quadratic invariants, Symplecticity, General linear methods, Hamiltonian systems.
AB - <p style="text-align: justify;">In this paper, we present some invariants and conservation laws of general linear methods applied to differential equation systems. We show that the quadratic invariants and symplecticity of the systems can be extended to general linear methods by a tensor product, and show that general linear methods with the matrix M=0 inherit in an extended sense the quadratic invariants possessed by the differential equation systems being integrated and preserve in an extended sense the symplectic structure of the phase space in the integration of Hamiltonian systems. These unify and extend existing relevant results on Runge-Kutta methods, linear multistep methods and one-leg methods. Finally, as special cases of general linear methods, we examine multistep Runge-Kutta methods, one-leg methods and linear two-step methods in detail. &nbsp;</p>