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 4 The results are obtained for \(\alpha =0.7\), \(x \in [-1,1]\), and \(t=1\)

N	n	M	\(L_{\infty }\)	\(error_{\mathit{est}}\)	ε	κ	C.time(s)
60	10	30	0.1103	5.37 × 10⁻¹	2.7	1.42 × 10⁺¹²	0.137554
		40	2.10 × 10⁻³	1.83 × 10⁻¹	2.7	1.42 × 10⁺¹²	0.194359
		60	5.01 × 10⁻⁴	2.12 × 10⁻²	2.7	1.42 × 10⁺¹²	0.557261
		70	1.03 × 10⁻⁴	2.40 × 10⁻³	2.7	1.42 × 10⁺¹²	3.174273
		90	8.49 × 10⁻⁵	8.18 × 10⁻⁴	2.7	1.42 × 10⁺¹²	5.439579
20	15	90	3.0 × 10⁻³	8.18 × 10⁻⁴	1.1	1.28 × 10⁺¹²	0.522960
40			3.37 × 10⁻⁴	8.18 × 10⁻⁴	2.2	2.14 × 10⁺¹²	2.770111
60			1.75 × 10⁻⁴	8.18 × 10⁻⁴	1.4	3.40 × 10⁺¹²	5.318668
70			8.76 × 10⁻⁵	8.18 × 10⁻⁴	4	1.24 × 10⁺¹²	6.681699
60	5	90	1.95 × 10⁻⁴	8.18 × 10⁻⁴	0.8	1.20 × 10⁺¹²	5.343147
	8		9.18 × 10⁻⁵	8.18 × 10⁻⁴	2.2	1.00 × 10⁺¹²	5.416387
	10		8.49 × 10⁻⁵	8.18 × 10⁻⁴	2.7	1.42 × 10⁺¹²	5.488575