Theory and Modern Applications
Table 5 The maximum error for \(N=1,\ldots, 12\), \(\lambda _{1}=2 \pi \), \(\lambda _{2}=2\pi \), and different values of the parameter α in Example 7.4
From: A fast numerical method for fractional partial differential equations
N | α = 0.2 | α = 0.4 | α = 0.6 | α = 0.8 | α = 1 |
|---|---|---|---|---|---|
1 | 2.6066.10−00 | 2.6051.10−00 | 2.6049.10−00 | 2.6092.10−00 | 2.6246.10−00 |
2 | 1.9083.10−00 | 1.9051.10−00 | 1.9295.10−00 | 1.9737.10−00 | 2.1794.10−00 |
3 | 8.3383.10−01 | 8.4028.10−01 | 8.6031.10−01 | 8.9811.10−01 | 9.8424.10−01 |
4 | 2.3551.10−01 | 2.4255.10−01 | 2.5659.10−01 | 2.8087.10−01 | 3.1023.10−01 |
5 | 5.8897.10−02 | 5.9052.10−02 | 5.9885.10−02 | 6.1600.10−02 | 6.2815.10−02 |
6 | 1.4284.10−02 | 1.4439.10−02 | 1.5317.10−02 | 1.6420.10−02 | 1.6707.10−02 |
7 | 2.1730.10−03 | 2.1986.10−03 | 2.2402.10−03 | 2.2673.10−03 | 2.2771.10−03 |
8 | 5.1272.10−04 | 5.2527.10−04 | 5.5008.10−04 | 5.8471.10−04 | 5.8723.10−04 |
9 | 6.0246.10−05 | 6.0782.10−05 | 6.1492.10−05 | 6.1423.10−05 | 6.1562.10−05 |
10 | 1.1860.10−05 | 1.2164.10−05 | 1.2624.10−05 | 1.3296.10−05 | 1.3345.10−05 |
11 | 1.1037.10−06 | 1.1065.10−06 | 1.1013.10−06 | 1.0874.10−06 | 1.0762.10−06 |
12 | 1.9317.10−07 | 1.9707.10−07 | 2.0332.10−07 | 2.1284.10−07 | 2.1485.10−07 |