The theory of matrix subdivision schemes provides tools for the analysis of general uniform stationary matrix schemes The special case of Hermite interpolatory subdivision schemes deals with re nement algorithms for the function and the derivatives values with matrix masks depending upon the re nement level i e non stationary matrix masks Here we rst show that a Hermite interpolatory subdivisio...

Hermite spectral methods are investigated for linear diffusion equations and the viscous Burgers’ equation in unbounded domains. When the solution domain is unbounded, the diffusion operator no longer has a compact resolvent, which makes the Hermite spectral methods unstable. To overcome this difficulty, a time-dependent scaling factor is employed in the Hermite expansions, which yields a posit...

We examine the use of Hermite interpolation, that is interpolation using derivative data, in place of Lagrange interpolation to develop high-order PDE solvers. The fundamental properties of Hermite interpolation are recalled, with an emphasis on their smoothing effect and robust performance for nonsmooth functions. Examples from the CHIDES library are presented to illustrate the construction an...

This paper deals with Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of di erential systems. Properties of Hermite matrix polynomials such as the three terms recurrence formula permit an e cient computation of matrix functions avoiding important computational drawbacks of other well-known methods. Results are applied to compute accurate approxi...