摘要：In this paper, we consider the space-fractional reaction–advection–diffusion equation with fractional diffusion and integer advection terms. By treating the first-order integer derivative as the composition of two Riemann–Liouville fractional derivative operators, we construct a fully discrete scheme by Legendre spectral method in a spatial and Crank–Nicolson scheme in temporal discretizations. Using thee right Riemann–Liouville fractional derivative, a novel duality argument is established, the optimal error estimate is proved to be O ( τ 2 + N − m ) $O( au^,+N^{-m})$ in L 2 $L^,$ -norm. Numerical tests are carried out to support the theoretical results, and the coefficient matrix with respect to first-order derivative obtained here is compared with that of traditional Legendre spectral method.
