Talk:Variational integrator

Order of the Integrator

From the article:

   since
   $L_{d}\left(t_{0},t_{1},q_{0},q_{1}\right)=\int _{t_{0}}^{t_{1}}dt\,L(t,q(t),v(t))+{\mathcal {O}}\left(t_{1}-t_{0}\right)^{3}$,
   our integrator will be second-order accurate.

May someone explain how to derive the second order? I mean, how does one obtain the ${\mathcal {O}}\left(t_{1}-t_{0}\right)^{3}$ term? The trapezoidal rule itself is only first order accurate.

--129.187.194.33 (talk) 12:24, 6 October 2016 (UTC)