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Theory and Modern Applications

Table 1 Comparison of numerical methods at \(\pmb{T=1.0}\) , \(\pmb{\Delta x=\Delta y=\frac{1}{10}}\) , \(\pmb{\alpha=0.25}\) , \(\pmb{\beta=0.45}\)

From: Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation

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CFDM in [ 21 ]

INM in [ 20 ]

Our method

1/10

1.5729e − 2

6.8179e − 3

5.1782e − 3

1/20

7.8976e − 3

3.6388e − 3

2.4390e − 3

1/40

3.9560e − 3

1.8825e − 3

1.1772e − 3

1/80

1.9794e − 3

9.3779e − 4

5.9755e − 4

1/160

9.8995e − 4

4.3872e − 4

3.3033e − 4