Piecewise discretization of monodromy operators of delay equations on adapted meshes

<p style='text-indent:20px;'>Periodic solutions of delay equations are usually approximated as continuous piecewise polynomials on meshes adapted to the solutions' profile. In practical computations this affects regularity (coefficients the) linearized system and, in turn, effectiveness assessing local stability by approximating Floquet multipliers. To overcome problem when computing multipliers collocation, discretization grid should include mesh computed periodic solution. By introducing a version existing pseudospectral techniques, we explain why and show experimentally that choice is essential presence either strong adaptation or nontrivial whose eigenfunctions' profile unrelated solution.</p>