A Hermite spectral method for fractional convection diffusion equations on unbounded domains. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: Yu, Hao; Wu, Boying; Zhang, Dazhi
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 10(2020)
• Page Start: 2142
• Page End: 2163
• Publication Date: 2020-10-02
• Subjects: The scaled Hermite function -- fractional convection diffusion equation -- fractional Laplacian equation -- unbounded domain -- spectral method; 65M70; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1683548
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, a Hermite spectral method is used for solving the fractional convection diffusion equations on unbounded domains. The scaled Hermite functions are used as basis functions, and the problems are solved in Fourier space. Multi-dimensional problems are considered in this paper, and the errors are estimated in Fourier space as well. At the end of the paper, the method is introduced to solve the fractional convection diffusion equations. Numerical examples are presented to verify our results.