Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Absolute errors for Example 1 by IRKM [31] at \(t=1\) when \(\alpha= 0.9\), \(N=100\), and \(\Delta t=0.001\)

From: A numerical investigation of Caputo time fractional Allen–Cahn equation using redefined cubic B-spline functions

z/t→	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
0.1	2.58 × 10⁻⁴	7.34 × 10⁻⁵	7.11 × 10⁻⁵	1.06 × 10⁻⁶	3.18 × 10⁻⁵	6.59 × 10⁻⁵	7.91 × 10⁻⁵	6.96 × 10⁻⁵	4.67 × 10⁻⁵
0.2	4.66 × 10⁻⁴	1.41 × 10⁻⁴	1.40 × 10⁻⁴	1.42 × 10⁻⁵	3.65 × 10⁻⁵	9.17 × 10⁻⁵	1.07 × 10⁻⁴	8.14 × 10⁻⁵	2.96 × 10⁻⁵
0.3	6.18 × 10⁻⁴	1.98 × 10⁻⁴	1.98 × 10⁻⁴	3.17 × 10⁻⁵	3.36 × 10⁻⁵	1.03 × 10⁻⁴	1.20 × 10⁻⁴	7.88 × 10⁻⁵	3.02 × 10⁻⁶
0.4	7.11 × 10⁻⁴	2.36 × 10⁻⁴	2.37 × 10⁻⁴	4.69 × 10⁻⁵	2.63 × 10⁻⁵	1.03 × 10⁻⁴	1.19 × 10⁻⁴	6.69 × 10⁻⁵	2.52 × 10⁻⁵
0.5	7.42 × 10⁻⁴	2.51 × 10⁻⁴	2.54 × 10⁻⁴	5.70 × 10⁻⁵	1.69 × 10⁻⁵	9.49 × 10⁻⁵	1.07 × 10⁻⁴	4.85 × 10⁻⁵	5.10 × 10⁻⁵
0.6	7.10 × 10⁻⁴	2.40 × 10⁻⁴	2.45 × 10⁻⁴	5.86 × 10⁻⁵	9.06 × 10⁻⁶	8.10 × 10⁻⁵	9.00 × 10⁻⁵	3.09 × 10⁻⁵	6.54 × 10⁻⁵
0.7	6.16 × 10⁻⁴	2.04 × 10⁻⁴	2.12 × 10⁻⁴	2.25 × 10⁻⁵	2.63 × 10⁻⁶	6.23 × 10⁻⁵	6.75 × 10⁻⁵	1.40 × 10⁻⁵	6.93 × 10⁻⁵
0.8	4.63 × 10⁻⁴	1.48 × 10⁻⁴	1.56 × 10⁻⁴	3.86 × 10⁻⁵	5.42 × 10⁻⁷	4.21 × 10⁻⁵	4.43 × 10⁻⁵	3.08 × 10⁻⁶	5.82 × 10⁻⁵
0.9	2.55 × 10⁻⁴	7.68 × 10⁻⁵	8.36 × 10⁻⁵	1.99 × 10⁻⁵	1.15 × 10⁻⁶	2.10 × 10⁻⁵	2.13 × 10⁻⁵	1.71 × 10⁻⁶	3.40 × 10⁻⁵

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