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Table 2 Numerical errors and convergence orders in spatial direction with \(\tau =\frac{1}{2000}\)

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