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 1 The results are obtained for \(\alpha =0.22111\), \(x \in [0,1]\), and \(t=1\)

N	n	M	\(L_{\infty }\)	\(error_{\mathit{est}}\)	ε	κ	C.time(s)
40	5	30	7.55 × 10⁻²	5.37 × 10⁻¹	1.9	1.14 × 10⁺¹⁰	0.229707
		40	1.10 × 10⁻³	1.83 × 10⁻¹	1.9	1.14 × 10⁺¹⁰	0.327267
		50	4.30 × 10⁻³	6.25 × 10⁻²	1.9	1.14 × 10⁺¹⁰	0.488246
		60	3.63 × 10⁻⁴	2.12 × 10⁻²	1.9	1.14 × 10⁺¹⁰	0.711818
		70	2.15 × 10⁻⁴	7.20 × 10⁻³	1.9	1.14 × 10⁺¹⁰	1.416137
		80	4.94 × 10⁻⁵	2.40 × 10⁻⁴	1.9	1.14 × 10⁺¹⁰	3.252525
		90	1.36 × 10⁻⁵	8.18 × 10⁻⁴	1.9	1.14 × 10⁺¹⁰	5.078051
60	5	90	4.84 × 10⁻⁵	8.18 × 10⁻⁴	2.9	1.06 × 10⁺¹⁰	9.992066
	10		8.73 × 10⁻⁵	8.18 × 10⁻⁴	7.4	1.18 × 10⁺¹⁰	7.996995
	15		5.99 × 10⁻⁴	8.18 × 10⁻⁴	8.9	1.02 × 10⁺¹⁰	10.601678
10	8	90	7.81 × 10⁻⁵	8.18 × 10⁻⁴	0.9	2.26 × 10⁺¹⁰	0.577473
20			2.97 × 10⁻⁵	8.18 × 10⁻⁴	2.0	1.18 × 10⁺¹⁰	1.026700
30			5.30 × 10⁻⁵	8.18 × 10⁻⁴	3.0	1.47 × 10⁺¹⁰	2.842371
35			8.95 × 10⁻⁵	8.18 × 10⁻⁴	3.6	1.10 × 10⁺¹⁰	4.340015