Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains (Communications in Computational Physics, 2020)
This work is concerned with spectral collocation methods for fractional PDEsin unbounded domains. The method consists of expanding the solution with properglobal basis functions and imposing collocation conditions on the Gauss-Hermite points.In this work, two Hermite-type functions are employed to serve as basis functions. Ourmain task is to find corresponding differentiation matrices which are computed recursively.Two important issues relevant to condition numbers and scaling factors will bediscussed. Applications of the spectral collocation methods to multi-term fractionalPDEs are also presented. Several numerical examples are carried out to demonstratethe effectiveness of the proposed methods.
Keywords: Fractional PDEs; Hermite polynomials/functions; unbounded domain; spectral collocation methods.