ABSTRACT
In this final chapter, we report a collage-style sketch of the ongoing research program related to the development of the theory of line integral methods. We exploit the discrete line integral tool to derive a few extensions of HBVMs for conserving multiple invariants in conservative systems. We also discuss the use of HBVMs to solve Hamiltonian boundary value problems. The extensions presented in this chapter are still under investigation and here we just report a mention to some preliminary results, hoping to convey the potentialities this new approach brings.
