Advances in Continuous and Discrete Models

Theory and Modern Applications

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

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