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Theory and Modern Applications

Table 3 Comparison of errors obtained for Example 1 with \(\tau=\frac {1}{512}\) and \(\alpha=0.1\)

From: Non-polynomial spline method for the time-fractional nonlinear Schrödinger equation

h

\(e_{\infty}(h,\tau)\) (real part)

\(e_{\infty}(h,\tau)\) (Imag. part)

Our method

[11]

Our method

[11]

1/4

3.6866388e − 2

4.2824e − 1

7.0575277e − 2

6.1335e − 1

1/9

1.2682659e − 3

7.0404e − 2

2.4249059e − 3

7.6325e − 2

1/14

2.2076538e − 4

2.1873e − 2

4.1971919e − 4

2.6096e − 2

1/19

6.5146969e − 5

1.0022e − 2

1.2268149e − 4

1.2230e − 2

1/24

2.5400339e − 5

5.1958e − 3

4.8342660e − 5

6.4207e − 3

1/29

1.1938367e − 5

2.8536e − 3

2.2621457e − 5

3.5662e − 3