Quispel G W, McLachlan R I. A new class of energy-preserving numerical integration methods[J]. Journal of Physics A: Mathematical and Theoretical, 2008, 41(4): 045206.
[2]
Feng K. Difference scheme for Hamilton formalism and symplectics geometry[J]. Journal of Computational Mathematics, 1986, 4(3): 279-289.
[3]
Feng K, Wu H M, Qin M Z, Wang D L. Construction of canonical difference scheme for Hamiltonian formalism via generating functions[J]. Journal of Computational Mathematics, 1989, 7(1): 71-96.
[4]
Liu X S, Su L W, Ding P Z. Symplectic algorithm for use in computing the time-independent Schr?inger equation[J]. International Journal of Quantum Chemistry, 2002, 87(1): 1-11.
Celledoni E. Energy-preserving integrators[J], Combinatorics and Control, 2010.
[7]
Celledoni E, McLachlan R I, Owren B, et al. Energy-preserving integrators and the structure of B-series[J]. Foundations of Computational Mathematics, 2010, 10(6): 673-693.
Guo B Y, Pascual P J. Numerical solution of the sine-Gordon equation[J]. Applied Mathematisc and Computation, 1986, 18(1): 1-14.
[13]
McLachlan R I, Quispel G W, Robidoux N. Geometric integration using discrete gradient[J]. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1999, 357(1754): 1021-1045.
[14]
Tang W S, Sun Y J. Time finite element methods: a unified framework for numerical discretizations of ODEs[J]. Applied Mathematisc and Computation, 2012, 219(4): 2158-2179.