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Theory and Modern Applications

Table 3 The \(L_{\infty }\), \(L_{2}\) errors and temporal convergence orders for Example 2

From: A high-order numerical scheme using orthogonal spline collocation for solving the two-dimensional fractional reaction–subdiffusion equation

α

N

\(L_{\infty }\) error

Convergence order

\(L_{2}\) error

Convergence order

0.1

10

2.1115e−006

 

1.2466e−006

 

15

4.3256e−007

3.9102

2.7478e−007

3.7296

20

1.5178e−007

3.6404

9.6187e−008

3.6487

25

6.9421e−008

3.5056

4.3264e−008

3.5805

30

3.7137e−008

3.4312

2.2759e−008

3.5232

0.3

10

3.0749e−006

 

1.8339e−006

 

15

7.8116e−007

3.3794

4.5271e−007

3.4502

20

3.0400e−007

3.2805

1.7241e−007

3.3557

25

1.4903e−007

3.1947

8.2694e−008

3.2926

30

8.3632e−008

3.1687

4.5743e−008

3.2476

0.5

10

3.9579e−006

 

2.2779e−006

 

15

1.0377e−006

3.3017

5.8315e−007

3.3605

20

4.1531e−007

3.1832

2.2726e−007

3.2757

25

2.0547e−007

3.1537

1.1073e−007

3.2221

30

1.1603e−007

3.1343

6.1945e−008

3.1858

0.7

10

3.9742e−006

 

2.2877e−006

 

15

1.0361e−006

3.3156

5.8263e−007

3.3733

20

4.1367e−007

3.1915

2.2639e−007

3.2859

25

2.0419e−007

3.1640

1.1009e−007

3.2309

30

1.1513e−007

3.1427

6.1505e−008

3.1931

0.9

10

2.5073e−006

 

1.5564e−006

 

15

6.1239e−007

3.4765

3.6906e−007

3.5494

20

2.3164e−007

3.3794

1.3617e−007

3.4658

25

1.1082e−007

3.3040

6.3868e−008

3.3928

30

6.1459e−008

3.2335

3.4746e−008

3.3389