Hermite spectral collocation methods for fractional PDEs in unbounded domains

2018/01/27 by Tao Tang, Tang, Tao, Huifang Yuan +3 · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1801.09073

openalex publication_date 2018/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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