An implicit wavelet collocation method for variable coefficients space fractional advection-diffusion equations

This paper studies a class of variable coefficients fractional advection-diffusion equations with two-sided space fractional derivatives in Caputo sense. By utilizing cubic semi-orthogonal B-spline wavelet collocation method (CSOBSWCM) in space combined with implicit Euler technique in time, an implicit wavelet collocation method is proposed to solve the fractional advection-diffusion equations in one and two dimensions. Next, we discuss a concrete realization of the novel method in which the operational matrix form of CSOBSWCM at each time step is provided. Moreover, we derive the unconditional stability and the convergence order of this numerical method. Finally, numerical examples are provided to verify the theoretical analysis of the present method.