Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 5 The results are obtained for \(\alpha =0.7\), \(x \in [0,1]\), and \(t=1\)

N	n	M	\(L_{\infty }\)	\(error_{\mathit{est}}\)	ε	κ	C.time(s)
70	15	30	6.70 × 10⁻³	5.37 × 10⁻¹	8.0	1.24 × 10⁺¹²	0.264581
		50	3.82 × 10⁻⁴	6.25 × 10⁻²	8.0	1.24 × 10⁺¹²	0.603418
		70	1.90 × 10⁻⁵	7.20 × 10⁻³	8.0	1.24 × 10⁺¹²	1.098719
		90	5.38 × 10⁻⁶	8.18 × 10⁻⁴	8.0	1.24 × 10⁺¹²	2.220157
30	10	80	2.06 × 10⁻⁵	2.40 × 10⁻³	2.7	1.08 × 10⁺¹²	0.800305
50			1.23 × 10⁻⁵	2.40 × 10⁻³	4.5	1.35 × 10⁺¹²	1.135721
70			2.22 × 10⁻⁵	2.40 × 10⁻³	6.4	1.15 × 10⁺¹²	1.567001
80			5.16 × 10⁻⁶	2.40 × 10⁻³	7.3	1.22 × 10⁺¹²	1.787725