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Theory and Modern Applications

Table 4 The \(L_{\infty }\), \(L_{2}\) errors and spatial 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

2.1200e−006

 

1.0669e−006

 

15

4.0685e−007

4.0712

1.9871e−007

4.1450

20

1.2876e−007

3.9992

6.1910e−008

4.0537

25

5.3905e−008

3.9021

2.5661e−008

3.9468

30

2.6096e−008

3.9789

1.2343e−008

4.0142

0.3

10

2.1275e−006

 

1.1076e−006

 

15

4.0785e−007

4.0738

2.0682e−007

4.1387

20

1.2899e−007

4.0015

6.4476e−008

4.0515

25

5.3983e−008

3.9036

2.6705e−008

3.9501

30

2.6127e−008

3.9803

1.2846e−008

4.0139

0.5

10

2.1313e−006

 

1.1321e−006

 

15

4.0836e−007

4.0752

2.1173e−007

4.1348

20

1.2912e−007

4.0024

6.6027e−008

4.0505

25

5.4022e−008

3.9049

2.7330e−008

3.9530

30

2.6143e−008

3.9809

1.3146e−008

4.0142

0.7

10

2.1275e−006

 

1.1196e−006

 

15

4.0786e−007

4.0738

2.0930e−007

4.1359

20

1.2900e−007

4.0013

6.5256e−008

4.0512

25

5.3981e−008

3.9041

2.7007e−008

3.9536

30

2.6126e−008

3.9803

1.2990e−008

4.0144

0.9

10

2.1120e−006

 

1.0507e−006

 

15

4.0582e−007

4.0681

1.9577e−007

4.1441

20

1.2851e−007

3.9971

6.0987e−008

4.0541

25

5.3822e−008

3.9003

2.5265e−008

3.9492

30

2.6062e−008

3.9776

1.2151e−008

4.0149