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Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains
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Year:    2018

Communications in Computational Physics, Vol. 24 (2018), Iss. 4 : pp. 1143–1168

Abstract

This work is concerned with spectral collocation methods for fractional PDEs in unbounded domains. The method consists of expanding the solution with proper global 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. Our main task is to find corresponding differentiation matrices which are computed recursively. Two important issues relevant to condition numbers and scaling factors will be discussed. Applications of the spectral collocation methods to multi-term fractional PDEs are also presented. Several numerical examples are carried out to demonstrate the effectiveness of the proposed methods.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2018.hh80.12

Communications in Computational Physics, Vol. 24 (2018), Iss. 4 : pp. 1143–1168

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Fractional PDEs Hermite polynomials/functions unbounded domain spectral collocation methods.

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