We study the order of convergence of Galerkin variational integrators for ordinary differential equations. Galerkin variational integrators approximate a variational (Lagrangian) problem by restricting the space of curves to the set of polynomials of degree at most $s$ and approximating the action integral using a quadrature rule. We show that, if the quadrature rule is sufficiently accurate, the order of the integrators thus obtained is $2s$.

翻译：我们研究了加勒金变异融合器对普通差异方程式的趋同顺序。加勒金变异融合器将曲线空间限制在一套多等量的高度,最多以美元计算,并使用四面形规则来接近集成动作。我们表明,如果四面形规则足够准确,那么由此获得的分解器的顺序是2美元。