Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 5 Absolute errors for Example 1 by the proposed method 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	3.05 × 10⁻⁶	3.57 × 10⁻⁶	3.67 × 10⁻⁶	3.66 × 10⁻⁶	3.65 × 10⁻⁶	3.67 × 10⁻⁶	3.75 × 10⁻⁶	3.94 × 10⁻⁶	4.28 × 10⁻⁶
0.2	5.76 × 10⁻⁶	6.76 × 10⁻⁶	6.95 × 10⁻⁶	6.94 × 10⁻⁶	6.92 × 10⁻⁶	6.96 × 10⁻⁶	7.13 × 10⁻⁶	7.83 × 10⁻⁶	8.20 × 10⁻⁶
0.3	7.88 × 10⁻⁶	9.26 × 10⁻⁶	9.52 × 10⁻⁶	9.51 × 10⁻⁶	9.49 × 10⁻⁶	9.56 × 10⁻⁶	9.81 × 10⁻⁶	1.01 × 10⁻⁵	1.14 × 10⁻⁵
0.4	9.22 × 10⁻⁶	1.08 × 10⁻⁵	1.11 × 10⁻⁵	1.11 × 10⁻⁵	1.11 × 10⁻⁵	1.12 × 10⁻⁵	1.15 × 10⁻⁵	1.22 × 10⁻⁵	1.34 × 10⁻⁵
0.5	9.67 × 10⁻⁶	1.14 × 10⁻⁵	1.17 × 10⁻⁵	1.17 × 10⁻⁵	1.17 × 10⁻⁵	1.18 × 10⁻⁵	1.21 × 10⁻⁵	1.28 × 10⁻⁵	1.42 × 10⁻⁵
0.6	9.22 × 10⁻⁶	1.08 × 10⁻⁵	1.11 × 10⁻⁵	1.11 × 10⁻⁵	1.11 × 10⁻⁵	1.12 × 10⁻⁵	1.15 × 10⁻⁵	1.22 × 10⁻⁵	1.34 × 10⁻⁵
0.7	7.88 × 10⁻⁶	9.26 × 10⁻⁶	9.52 × 10⁻⁶	9.51 × 10⁻⁶	9.49 × 10⁻⁶	9.56 × 10⁻⁶	9.81 × 10⁻⁶	1.01 × 10⁻⁵	1.14 × 10⁻⁵
0.8	5.76 × 10⁻⁶	6.76 × 10⁻⁶	6.95 × 10⁻⁶	6.94 × 10⁻⁶	6.92 × 10⁻⁶	6.96 × 10⁻⁶	7.13 × 10⁻⁶	7.83 × 10⁻⁶	8.20 × 10⁻⁶
0.9	3.05 × 10⁻⁶	3.57 × 10⁻⁶	3.67 × 10⁻⁶	3.66 × 10⁻⁶	3.65 × 10⁻⁶	3.67 × 10⁻⁶	3.75 × 10⁻⁶	3.94 × 10⁻⁶	4.28 × 10⁻⁶

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