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Table 3 Maximum absolute errors for \(N=5\) and different choices of \(\mathfrak{h}(t)\) and \(\sigma (x, t)\) for Example 6.2

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

\(\mathfrak{h}(t)=t\) σ(x,t)=1.25 σ(x,t)=1.50 σ(x,t)=1.75 \(\sigma (x,t)=2-0.2e^{-xt}\)
MAE 1.4000 × 10−18 5.4920 × 10−17 1.9500 × 10−18 1.8800 × 10−18
\(\mathfrak{h}(t)=t^{2}+1\) σ(x,t)=1.25 σ(x,t)=1.50 σ(x,t)=1.75 \(\sigma (x,t)=2-0.2e^{-xt}\)
MAE 3.1600 × 10−18 4.3200 × 10−18 1.0168 × 10−18 1.9856 × 10−18
\(\mathfrak{h}(t)=\cos (t)\) σ(x,t)=1.25 σ(x,t)=1.50 σ(x,t)=1.75 \(\sigma (x,t)=2-0.2e^{-xt}\)
MAE 9.9203 × 10−9 3.0399 × 10−9 2.9478 × 10−9 3.8210 × 10−9
\(\mathfrak{h}(t)=\sin (t)\) σ(x,t)=1.25 σ(x,t)=1.50 σ(x,t)=1.75 \(\sigma (x,t)=2-0.2e^{-xt}\)
MAE 3.9225 × 10−4 5.9571 × 10−6 2.4618 × 10−8 5.3379 × 10−9