A Hermite spectral method for fractional convection diffusion equations on unbounded domains

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.

Keywords:

• The scaled Hermite function
• fractional convection diffusion equation
• fractional Laplacian equation
• unbounded domain
• spectral method

2010 Mathematics Subject Classification:

• 65M70

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (Grant No. U1637208), National Key Research and Development Program of China (2017YFB1401801), Natural Scientific Foundation of Heilongjiang Province in China (A2016003) and Research Project of China Scholarship Council (No. 201706120212).