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Table 1 Results extracted via the presented approach for Example 1 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
5 4 4.8716E-03 4.8703E-03 4.8704E-03 02.54
6 5 4.3022E-04 07.2127 4.3018E-04 07.2122 4.3018E-04 07.2122 05.29
7 6 3.2230E-05 09.0078 3.2171E-05 09.0139 3.2179E-05 09.0130 12.71
8 7 2.6413E-06 09.9541 2.6412E-06 09.9470 2.6379E-06 09.9529 31.04
9 8 1.9235E-07 11.7400 2.1424E-07 11.2568 2.1424E-07 11.2512 64.64