Abstract
In the present work, a compact difference scheme with convergence order O(τ2 + h4) is proposed for the fourth-order fractional sub-diffusion equation, where h and τ are space and temporal step length, respectively. The method is based on applying the L2−1σ formula to approximate the time Caputo fractional derivative and employing compact operator to approximate the spatial fourth-order derivative. Using the special properties of L2−1σ formula and mathematical induction method, we obtain the unconditional stability and convergence for our scheme by discrete energy method. Furthermore, the extension to the two-dimensional case is also considered. Numerical examples are given to verify the theoretical analysis and efficiency of the new developed scheme.
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