# Functional equivariance and conservation laws in numerical integration

@article{McLachlan2021FunctionalEA, title={Functional equivariance and conservation laws in numerical integration}, author={Robert I. McLachlan and Ari Stern}, journal={ArXiv}, year={2021}, volume={abs/2111.10042} }

. Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important properties of the system. For example, a time-evolution PDE may have an observable that satisﬁes a local conservation law, such as the multisymplectic conservation law for Hamiltonian PDEs. We introduce the concept of functional equivariance , a natural sense…

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