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From the article:

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

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

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