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Based on the weighted and shifted Grünwald operator, a new high-order compact finite difference scheme is derived for the fractional sub-diffusion equation. It is proved that the difference scheme is unconditionally stable and convergent in $$L_{\infty }$$ L ∞ -norm by the energy method. The convergence order is $$O(\tau ^3+h^4)$$ O ( τ 3 + h 4 ) , where $$\tau $$ τ ...
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