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Table 1 Error, order of accuracy with different values of \(\alpha _{x}\) and \(\alpha _{y}\) for Example 1

From: Stable finite difference method for fractional reaction–diffusion equations by compact implicit integration factor methods

  \(\alpha _{x}=\alpha _{y}=1.4\) \(\alpha _{x}=1.4\), \(\alpha _{y}=1.8\) \(\alpha _{x}=\alpha _{y}=1.8\)
\(N_{x}\times N_{y}\) \(L^{2}\) error Order \(L^{2}\) error Order \(L^{2}\) error Order
16 × 16 1.13 × 10−5 1.18 × 10−5 1.18 × 10−5
32 × 32 2.75 × 10−6 2.02 2.86 × 10−6 2.03 2.85 × 10−6 2.03
64 × 64 6.74 × 10−7 2.02 7.07 × 10−7 2.01 7.09 × 10−7 2.00
128 × 128 1.68 × 10−7 2.00 1.75 × 10−7 2.01 1.78 × 10−7 2.00