  In this paper, a class of high-order methods to numerically solve Functional
Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is
discussed. The framework stems from the expansion of the vector field
associated with the reference differential equation along the shifted and
scaled Legendre polynomial orthonormal basis, working on a suitable extension
of Hamiltonian Boundary Value Methods. Within the design of the methods, a
proper generalization of the perturbation results coming from the field of
ordinary differential equations is considered, with the aim of handling the
case of FDEPCAs. The error analysis of the devised family of methods is
performed, while a few numerical tests on Hamiltonian FDEPCAs are provided, to
give evidence to the theoretical findings and show the effectiveness of the
obtained resolution strategy.
