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 2 The results are obtained for \(\alpha =0.3321\), \(x \in [0,1]\), and \(t=1\)

N	n	M	\(L_{\infty }\)	\(error_{\mathit{est}}\)	ε	κ	C.time(s)
45	5	30	1.10 × 10⁻¹	5.37 × 10⁻¹	2.1	1.34 × 10⁺¹⁰	0.133238
		50	5.30 × 10⁻³	6.25 × 10⁻²	2.1	1.34 × 10⁺¹⁰	0.296257
		70	2.27 × 10⁻⁴	7.20 × 10⁻³	2.1	1.34 × 10⁺¹⁰	0.620503
		90	8.22 × 10⁻⁵	8.18 × 10⁻⁴	2.1	1.34 × 10⁺¹⁰	3.566523
40	5	90	4.78 × 10⁻⁴	8.18 × 10⁻⁴	1.08	1.01 × 10⁺¹²	2.989985
	8		8.31 × 10⁻⁵	8.18 × 10⁻⁴	2.9	1.04 × 10⁺¹²	3.039480
	10		7.93 × 10⁻⁵	8.18 × 10⁻⁴	3.65	1.0 × 10⁺¹²	2.642598
35	9	90	1.10 × 10⁻⁴	8.18 × 10⁻⁴	2.88	1.03 × 10⁺¹²	2.187149
40		90	5.54 × 10⁻⁵	8.18 × 10⁻⁴	3.31	1.0 × 10⁺¹²	2.800518
50		90	9.07 × 10⁻⁵	8.18 × 10⁻⁴	4.16	1.0 × 10⁺¹²	4.435288