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Theory and Modern Applications

Table 4 The maximum error for \(N=1,\ldots, 12\), \(\lambda _{1}= \pi \), \(\lambda _{2}=\pi \), 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

1.1071.10−00

1.0950.10−00

1.1195.10−00

1.1775.10−00

1.24181.10−00

2

2.5455.10−01

2.4974.10−01

2.4349.10−01

2.3504.10−01

2.4172.10−01

3

6.0042.10−02

6.0495.10−02

6.1587.10−02

6.4331.10−02

7.2937.10−02

4

7.0736.10−03

7.0861.10−03

7.1905.10−03

7.4401.10−03

7.7583.10−03

5

1.2911.10−03

1.2991.10−03

1.3180.10−03

1.2873.10−03

1.2696.10−03

6

9.8780.10−05

9.8462.10−05

9.8370.10−05

9.9410.10−05

1.0110.10−04

7

1.4229.10−05

1.4201.10−05

1.4315.10−05

1.4212.10−05

1.3889.10−05

8

7.8316.10−07

7.8472.10−07

7.9093.10−07

7.9484.10−07

8.0049.10−07

9

9.8294.10−08

9.7810.10−08

9.7654.10−08

9.6831.10−08

9.5299.10−08

10

4.3006.10−09

4.2961.10−09

4.3060.10−09

4.3251.10−09

4.3391.10−09

11

4.5641.10−10

4.5733.10−10

4.5784.10−10

4.5211.10−10

4.4670.10−10

12

1.6370.10−11

1.6392.10−11

1.6451.10−11

1.6487.10−11

1.6526.10−11