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Table 2 Absolute errors for \(N=4\) at equally spaced points \((x_{j}, t_{j})\) for Example 6.1

From: Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel

\((x_{j}, t_{j})\) \(\sigma _{1}(x, t)=1\) \(\sigma _{2}(x, t)=0.875\) \(\sigma _{3}(x, t)\)
\(\mathfrak{h}(t)=t \) \(\mathfrak{h}(t)=e^{t^{2}}\) \(\mathfrak{h}(t)=t \) \(\mathfrak{h}(t)=e^{t^{2}}\) \(\mathfrak{h}(t)=t\) \(\mathfrak{h}(t)=e^{t^{2}}\)
(0.0, 0.0) 0.00 0.00 0.00 0.00 0.00  
(0.1, 0.1) 2.90 × 10−22 1.70 × 10−22 1.90 × 10−21 3.00 × 10−22 1.90 × 10−21 4.24 × 10−21
(0.2, 0.2) 9.00 × 10−22 3.30 × 10−21 9.10 × 10−21 3.50 × 10−21 7.80 × 10−21 1.16 × 10−20
(0.3, 0.3) 5.00 × 10−21 1.80 × 10−20 1.90 × 10−20 1.30 × 10−20 1.30 × 10−20 1.00 × 10−21
(0.4, 0.4) 9.00 × 10−21 3.80 × 10−20 8.20 × 10−20 2.10 × 10−20 1.70 × 10−20 2.00 × 10−20
(0.5, 0.5) 2.00 × 10−20 5.00 × 10−20 1.20 × 10−19 3.00 × 10−20 1.00 × 10−20 3.00 × 10−20
(0.6, 0.6) 3.00 × 10−20 4.00 × 10−20 4.00 × 10−20 1.00 × 10−20 2.00 × 10−20 1.00 × 10−20
(0.7, 0.7) 3.00 × 10−20 1.00 × 10−20 2.90 × 10−19 0.00 8.00 × 10−20 1.00 × 10−19
(0.8, 0.8) 3.00 × 10−20 0.00 1.51 × 10−18 1.00 × 10−20 2.60 × 10−19 2.00 × 10−19
(0.9, 0.9) 2.00 × 10−20 5.00 × 10−20 5.68 × 10−18 1.00 × 10−20 9.70 × 10−19 1.40 × 10−19
(1.0, 1.0) 0.00 2.00 × 10−19 1.71 × 10−17 2.00 × 10−20 3.90 × 10−18 4.00 × 10−19