Theory and Modern Applications
From: An efficient numerical algorithm for solving the two-dimensional fractional cable equation
\(h_{x}=h_{y}\) | \(e_{2}(h,\tau)\) | rate 3 | \(e_{\infty }(h,\tau)\) | rate 4 | |
---|---|---|---|---|---|
\(\gamma _{1}=0.9\), \(\gamma _{2}=0.8\) | 1/4 | 7.0259e-4 | ∗ | 1.4052e-3 | ∗ |
1/8 | 4.3084e-5 | 4.0274 | 8.6167e-5 | 4.0275 | |
1/16 | 2.6514e-6 | 4.0223 | 5.3027e-6 | 4.0223 | |
1/32 | 1.3649e-7 | 4.2798 | 2.7299e-7 | 4.2798 | |
\(\gamma _{1}=0.8\), \(\gamma _{2}=0.6\) | 1/4 | 7.0294e-4 | ∗ | 1.4059e-3 | ∗ |
1/8 | 4.3105e-5 | 4.0275 | 8.6210e-5 | 4.0274 | |
1/16 | 2.6527e-6 | 4.0223 | 5.3054e-6 | 4.0223 | |
1/32 | 1.3656e-7 | 4.2799 | 2.7312e-7 | 4.2798 | |
\(\gamma _{1}=0.6\), \(\gamma _{2}=0.2\) | 1/4 | 7.0338e-4 | ∗ | 1.4067e-3 | ∗ |
1/8 | 4.3132e-5 | 4.0274 | 8.6265e-5 | 4.0274 | |
1/16 | 2.6547e-6 | 4.0221 | 5.3095e-6 | 4.0221 | |
1/32 | 1.3705e-7 | 4.2757 | 2.7411e-7 | 4.2757 | |
\(\gamma _{1}=0.2\), \(\gamma _{2}=0.6\) | 1/4 | 7.4232e-4 | ∗ | 1.4846e-3 | ∗ |
1/8 | 4.5522e-5 | 4.0274 | 9.1044e-5 | 4.0274 | |
1/16 | 2.8069e-6 | 4.0195 | 5.6139e-6 | 4.0194 | |
1/32 | 1.5015e-7 | 4.2245 | 3.0031e-7 | 4.2245 |