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Theory and Modern Applications

Table 5 Absolute errors of \(\pmb{x(t)}\) at \(\pmb{\nu=1.1}\) , \(\pmb{\alpha=\beta=1}\) and various choices of N for Example 3

From: An efficient numerical scheme based on the shifted orthonormal Jacobi polynomials for solving fractional optimal control problems

t

N  = 5

N  = 10

N  = 15

N  = 20

0.0

1.00422⋅10−5

8.29649⋅10−8

4.23110⋅10−9

4.50878⋅10−10

0.1

7.49108⋅10−6

3.01896⋅10−8

1.68037⋅10−9

1.31765⋅10−10

0.2

3.42018⋅10−6

3.13243⋅10−8

6.73807⋅10−10

7.12029⋅10−11

0.3

3.35072⋅10−6

6.43527⋅10−10

5.68312⋅10−10

1.09513⋅10−10

0.4

5.03449⋅10−6

1.60609⋅10−8

1.78891⋅10−10

4.67566⋅10−11

0.5

1.46457⋅10−6

2.65655⋅10−8

5.18689⋅10−10

6.49534⋅10−11

0.6

3.40168⋅10−6

2.74590⋅10−9

2.41793⋅10−10

9.48547⋅10−11

0.7

4.97962⋅10−6

1.00729⋅10−8

4.07278⋅10−10

3.64302⋅10−11

0.8

1.55387⋅10−6

2.19671⋅10−8

2.53742⋅10−10

3.72208⋅10−11

0.9

2.22496⋅10−6

8.30311⋅10−9

4.31625⋅10−10

3.08854⋅10−11

1.0

8.15620⋅10−6

9.66660⋅10−8

7.88301⋅10−9

1.15540⋅10−9