A Crank-Nicolson fourth-order fractional centered difference scheme for multi-dimensional variable-coefficient Riesz space fractional diffusion equations is proven stable and convergent, and a sine-transform preconditioner gives PCG a mesh-size-independent iteration count.
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An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients
A Crank-Nicolson fourth-order fractional centered difference scheme for multi-dimensional variable-coefficient Riesz space fractional diffusion equations is proven stable and convergent, and a sine-transform preconditioner gives PCG a mesh-size-independent iteration count.