Theory and Modern Applications
From: An efficient numerical algorithm for solving the two-dimensional fractional cable equation
Ï„ | \(e_{2}(h,\tau)\) | 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 |