Volume 24, Issue 4
Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains

Commun. Comput. Phys., 24 (2018), pp. 1143-1168.

Published online: 2018-06

[An open-access article; the PDF is free to any online user.]

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• 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.

• Keywords

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

33C45, 34K37, 35R11, 65M70

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• RIS
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@Article{CiCP-24-1143, author = {}, title = {Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {4}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2018.hh80.12}, url = {http://global-sci.org/intro/article_detail/cicp/12322.html} }
TY - JOUR T1 - Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains JO - Communications in Computational Physics VL - 4 SP - 1143 EP - 1168 PY - 2018 DA - 2018/06 SN - 24 DO - http://doi.org/10.4208/cicp.2018.hh80.12 UR - https://global-sci.org/intro/article_detail/cicp/12322.html KW - Fractional PDEs, Hermite polynomials/functions, unbounded domain, spectral collocation methods. AB -

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.

Tao Tang, Huifang Yuan & Tao Zhou. (2020). Hermite Spectral Collocation Methods for Fractional PDEs in Unbounded Domains. Communications in Computational Physics. 24 (4). 1143-1168. doi:10.4208/cicp.2018.hh80.12
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