Solving spatial-fractional partial differential diffusion equations by spectral method

Abstract

This paper focuses on numerical solution of an initial-boundary value problem of spatial-fractional partial differential diffusion equation. The proposed numerical method is based on Legendre spectral method for Riemann–Liouville fractional derivative in space and a finite difference scheme in time. Numerical analysis of stability and convergence for our method is established rigourously. Finally, numerical results verify the validity of the theoretical analysis.

Keywords:

• spatial-fractional partial differential diffusion equation
• spectral method
• Riemann–Liouville derivatives
• stability
• convergence

Acknowledgements

This research is supported by the National Center for Mathematics and Interdisciplinary Sciences, and by National Natural Science Foundation of China (Grant Nos. 60931002, 91130019, 11001072 and 11101381).