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Theory and Modern Applications

Table 2 Results extracted via the presented approach for Example 2 with three choices of \(\zeta (\tau )\)

From: An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

M

N

ζ(τ)=0.50 + 0.25sin(τ)

\(\zeta (\tau )=0.85-0.25e^{-\tau}\)

\(\zeta (\tau )=0.65+0.25\tau ^{3}\cos (\tau )\)

CPU time

\(e_{\theta}\)

CO

\(e_{\theta}\)

CO

\(e_{\theta}\)

CO

4

4

1.6710E-03

–

1.6731E-03

–

1.6713E-03

–

05.70

5

5

1.6538E-04

06.3430

1.6555E-04

06.3436

1.6540E-04

06.3431

12.96

6

6

6.7121E-06

10.3935

6.7288E-06

10.3887

6.7221E-06

10.3890

23.78

7

7

6.8627E-07

08.5388

6.8598E-07

08.5496

6.8298E-07

08.5623

51.53

8

8

1.5974E-08

15.9628

1.5855E-08

15.9928

1.5414E-08

16.0939

92.15