  In this article we study the numerical approximation of a variable
coefficient fractional diffusion equation. Using a change of variable, the
variable coefficient fractional diffusion equation is transformed into a
constant coefficient fractional diffusion equation of the same order. The
transformed equation retains the desirable stability property of being an
elliptic equation. A spectral approximation scheme is proposed and analyzed for
the transformed equation, with error estimates for the approximated solution
derived. An approximation to the unknown of the variable coefficient fractional
diffusion equation is then obtained by post processing the computed
approximation to the transformed equation. Error estimates are also presented
for the approximation to the unknown of the variable coefficient equation with
both smooth and non-smooth diffusivity coefficient and right-hand side. Three
numerical experiments are given whose convergence results are in strong
agreement with the theoretically derived estimates.
