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Table 1 Maximum errors and temporal convergence orders for the ADI–implicit Euler method with \(T_{\mathrm{end}}=1\)

From: Alternating-direction implicit finite difference methods for a new two-dimensional two-sided space-fractional diffusion equation

\(\Delta t=h_{1}=h_{2}\) α = 0.6, β = 0.8 α = 0.7, β = 0.9
Maximum error Order Maximum error Order
1/10 4.8003e−3 - 1.7678e−3 -
1/20 2.6001e−3 0.885 8.8503e−4 0.999
1/40 1.3000e−3 1.000 4.4357e−4 0.996
1/80 6.7261e−4 0.956 2.2553e−4 0.976