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Table 1 Numerical errors and convergence orders in time direction with \(h=\frac{1}{128}\)

From: An efficient numerical algorithm for solving the two-dimensional fractional cable equation

  τ \(e_{2}(h,\tau)\) rate 1 \(e_{\infty }(h,\tau)\) rate 2
\(\gamma _{1}=0.9\), \(\gamma _{2}=0.8\) 1/20 3.1063e-4 6.2126e-4
1/40 7.7663e-5 1.9999 1.5532e-4 1.9998
1/80 1.9416e-5 2.0000 3.8832e-5 1.9999
1/160 4.8537e-6 2.0001 9.7074e-6 2.0001
\(\gamma _{1}=0.8\), \(\gamma _{2}=0.6\) 1/20 3.0836e-4 6.1672e-4
1/40 7.7136e-5 1.9991 1.5427e-4 1.9991
1/80 1.9291e-5 1.9995 3.8582e-5 1.9995
1/160 4.8233e-6 1.9998 9.6467e-6 1.9998
\(\gamma _{1}=0.6\), \(\gamma _{2}=0.2\) 1/20 2.9879e-4 5.9758e-4
1/40 7.5111e-5 1.9920 1.5022e-4 1.9920
1/80 1.8851e-5 1.9944 3.7702e-5 1.9944
1/160 4.7253e-6 1.9961 9.4507e-6 1.9965
\(\gamma _{1}=0.2\), \(\gamma _{2}=0.6\) 1/20 2.1680e-4 4.3360e-4
1/40 5.6905e-5 1.9297 1.1381e-4 1.9297
1/80 1.4814e-5 1.9415 2.9629e-5 1.9415
1/160 3.8312e-6 1.9511 7.6624e-6 1.9511