We introduce conservative integrators for long term integration of piecewise smooth systems with transversal dynamics and piecewise smooth conserved quantities. In essence, for a piecewise dynamical system with piecewise defined conserved quantities such that its trajectories cross transversally to its interface, we combine Mannshardt's transition scheme and the Discrete Multiplier Method to obtain conservative integrators capable of preserving conserved quantities up to machine precision and accuracy order. We prove that the order of accuracy of the integrators is preserved after crossing the discontinuity in the case of codimension one number of conserved quantities. Numerical examples illustrate the preservation of accuracy order.

翻译：我们引入了保守的集成器,以便长期整合具有横向动态和节能节能数量的整片光滑系统。 本质上,对于一个带有条形定义的节能系统,其轨迹跨过其接口的条状节水量,我们将曼沙特的过渡计划和分解倍增法结合起来,以获得能够将节能数量保存到机器精确度和精确度的保守集成器。 我们证明,在混合了一定数量的节能量时,集成器的准确性在跨越了不连续性之后得到了维护。 数字示例说明了准确性秩序的维护。