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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