Thomas Hagstrom
Department of Mathematics
Southern Methodist University
Dallas, USA
An amazing property of Hermite interpolation is that it is a projection in a Sobolev seminorm. As a result, in constrast with the usual Lagrange interpolant, Hermite interpolation has a smoothing eect. We show how to exploit this projection property to develop Hermite-based solvers for differential equations with novel properties. For hyperbolic pdes, Hermite methods admit order-independent time steps and highly localized evolution processes which can be exploited on modern computer architectures. For initial value problems one can develop implicit schemes of arbitrary order for which the system size is also order-independent.