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Theory and Modern Applications

Table 2 Absolute errors for Example 1 by IRKM [31] at \(t=1\) when \(\alpha= 0.7\), \(N=100\), 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

3.23 × 10−4

4.72 × 10−5

3.74 × 10−5

3.31 × 10−5

4.38 × 10−5

6.78 × 10−5

7.25 × 10−5

8.87 × 10−5

5.08 × 10−5

0.2

5.82 × 10−4

9.50 × 10−5

7.91 × 10−5

4.43 × 10−5

5.85 × 10−5

9.51 × 10−5

9.65 × 10−5

1.17 × 10−4

4.09 × 10−5

0.3

7.70 × 10−4

1.36 × 10−4

1.14 × 10−4

4.80 × 10−5

6.41 × 10−5

1.08 × 10−4

1.06 × 10−4

1.28 × 10−4

2.22 × 10−5

0.4

8.85 × 10−4

1.64 × 10−4

1.39 × 10−4

4.66 × 10−5

6.28 × 10−5

1.10 × 10−4

1.04 × 10−4

1.27 × 10−4

5.79 × 10−7

0.5

9.24 × 10−4

1.75 × 10−4

1.51 × 10−4

4.18 × 10−5

5.62 × 10−5

1.03 × 10−5

9.40 × 10−5

1.13 × 10−4

2.09 × 10−5

0.6

8.85 × 10−4

1.68 × 10−4

1.47 × 10−4

3.59 × 10−5

4.70 × 10−5

9.03 × 10−5

7.87 × 10−5

9.52 × 10−5

3.54 × 10−5

0.7

7.69 × 10−4

1.42 × 10−4

1.28 × 10−4

2.87 × 10−5

3.56 × 10−5

7.14 × 10−5

5.90 × 10−5

7.14 × 10−5

4.31 × 10−5

0.8

5.79 × 10−4

1.01 × 10−4

9.52 × 10−5

2.09 × 10−5

2.37 × 10−5

4.96 × 10−5

3.86 × 10−5

4.68 × 10−5

3.96 × 10−5

0.9

3.21 × 10−4

5.12 × 10−5

5.08 × 10−5

1.17 × 10−5

1.17 × 10−5

2.54 × 10−5

1.85 × 10−5

2.25 × 10−5

2.52 × 10−5