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Table 4 Numerical results of the Example 2 for \(\alpha=1.4\)

From: A medium-shifted splitting iteration method for a diagonal-plus-Toeplitz linear system from spatial fractional Schrödinger equations

Method

 

M

 

800

1600

3200

5000

10,000

20,000

PMS2

IT

3

3

3

3

3

3

CPU (s)

0.2488

0.9239

3.2826

7.3958

24.7668

126.0364

Error

1.353e − 07

1.328e − 07

1.586e − 07

2.159e − 07

3.254e − 07

5.434e − 07

PMS1

IT

3

3

3

3

3

3

CPU (s)

0.1666

1.1425

5.1075

12.1415

68.6869

351.8482

Error

1.353e − 07

1.328e − 07

1.586e − 07

2.160e − 07

3.255e − 07

5.444e − 07

MS2

IT

3

3

3

3

3

3

CPU (s)

0.2034

1.5269

8.6382

63.1743

221.7870

7645.00

Error

1.354e − 07

1.327e − 07

1.586e − 07

2.159e − 07

3.255e − 07

5.615e − 07

MS1

IT

3

3

3

3

3

3

CPU (s)

0.1969

1.0012

4.9433

12.3412

67.0036

385.5151

Error

1.354e − 07

1.327e − 07

1.586e − 07

2.159e − 07

3.255e − 07

5.533e − 07

SOR

IT

10

21

62

153

695

CPU (s)

0.3228

4.8402

98.6408

723.7896

1854.10

Error

5.590e − 07

8.608e − 07

9.952e − 07

9.960e − 07

9.900e − 07