On the Infinite Order Limit of Hermite-based Finite Difference Schemes

Pseudospectral (PS) methods are widely used for solving partial differential equations (PDEs) to high accuracy in simple geometries. They can be seen as the limit of finite difference methods for increasing order of accuracy. Similarly, recently introduced Hermite-based finite difference approximations converge to Hermite-based pseudospectral (HPS) limits. We derive here HPS coefficients and make comparisons between PS and HPS approximations....