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 3 The results are obtained for \(\alpha =0.3\), \(x \in [-1,1]\), and \(t=1\)

N	n	M	\(L_{\infty }\)	\(error_{\mathit{est}}\)	ε	κ	C.time(s)
60	10	30	0.1103	0.5373	2.7	1.42 × 10⁺¹²	0.118417
		50	6.30 × 10⁻³	6.25 × 10⁻²	2.7	1.42 × 10⁺¹²	0.325090
		70	3.42 × 10⁻⁴	7.20 × 10⁻³	2.7	1.42 × 10⁺¹²	1.494413
		90	8.67 × 10⁻⁵	8.18 × 10⁻⁴	2.7	1.42 × 10⁺¹²	5.319907
		100	8.53 × 10⁻⁵	2.76 × 10⁻⁴	2.7	1.42 × 10⁺¹²	8.300325
10	10	90	0.1088	8.18 × 10⁻⁴	0.4	2.26 × 10⁺¹²	0.318351
30			4.84 × 10⁻⁴	8.18 × 10⁻⁴	1.3	1.97 × 10⁺¹²	0.993061
50			1.64 × 10⁻⁴	8.18 × 10⁻⁴	2.2	1.93 × 10⁺¹²	4.045085
60			8.67 × 10⁻⁵	8.18 × 10⁻⁴	2.7	1.42 × 10⁺¹²	5.298335
80	10	100	1.92 × 10⁻⁴	2.76 × 10⁻⁴	3.6	1.52 × 10⁺¹²	11.975305
	15		1.24 × 10⁻⁴	2.76 × 10⁻⁴	4.6	1.14 × 10⁺¹²	12.048443
	20		4.90 × 10⁻⁵	2.76 × 10⁻⁴	5.0	1.13 × 10⁺¹²	12.145290