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Solving spatial-fractional partial differential diffusion equations by spectral method

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.