Discretization of polynomial vector fields by polarization

作者：Celledoni Elena; McLachlan Robert I^*; McLaren David I; Owren Brynjulf; Quispel G R W

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2015, 471(2184): 20150390.

DOI：10.1098/rspa.2015.0390

• geometric integration
• Kahan's method
• polarization

A novel integration method for quadratic vector fields was introduced by Kahan in 1993. Subsequently, it was shown that Kahan's method preserves a (modified) measure and energy when applied to quadratic Hamiltonian vector fields. Here we generalize Kahan's method to cubic resp. higher degree polynomial vector fields and show that the resulting discretization also preserves modified versions of the measure and energy when applied to cubic resp. higher degree polynomial Hamiltonian vector fields.

• 出版日期2015-12-8