This paper examines functional equivariance, recently introduced by McLachlan and Stern [Found. Comput. Math. (2022)], from the perspective of backward error analysis. We characterize the evolution of certain classes of observables (especially affine and quadratic) by structure-preserving numerical integrators in terms of their modified vector fields. Several results on invariant preservation and symplecticity of modified vector fields are thereby generalized to describe the numerical evolution of non-invariant observables.

翻译：本文从向后误差分析的角度研究McLachlan和Stern[Found. Comput. Math. (2022)]近期提出的功能等变性。我们通过结构保持数值积分器的修正向量场，刻画了特定可观测类（特别是仿射和二次型）的演化过程。由此将修正向量场的不变量保持性和辛性等若干结论加以推广，用以描述非不变可观测量的数值演化。