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Theory and Modern Applications

Table 5 The \(L_{\infty }\), \(L_{2}\) errors and temporal convergence orders for Example 3

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

1.2104e−009

 

6.1520e−010

 

15

3.2755e−010

3.2236

1.6621e−010

3.2276

20

1.3151e−010

3.1721

6.6547e−011

3.1818

25

6.5042e−011

3.1551

3.2911e−011

3.1554

30

3.6739e−011

3.1329

1.8572e−011

3.1381

0.3

10

7.4096e−009

 

3.7525e−009

 

15

2.0211e−009

3.2041

1.0218e−009

3.2083

20

8.1469e−010

3.1583

4.1068e−010

3.1685

25

4.0374e−010

3.1461

2.0351e−010

3.1464

30

2.2832e−010

3.1265

1.1497e−010

3.1321

0.5

10

1.8082e−008

 

9.1348e−009

 

15

4.9358e−009

3.2023

2.4893e−009

3.2064

20

1.9989e−009

3.1421

1.0052e−009

3.1521

25

9.9552e−010

3.1239

5.0063e−010

3.1239

30

5.6561e−010

3.1009

2.8416e−010

3.1062

0.7

10

3.0948e−008

 

1.5614e−008

 

15

8.3625e−009

3.2273

4.2128e−009

3.2310

20

3.3879e−009

3.1408

1.7019e−009

3.1506

25

1.6904e−009

3.1157

8.4920e−010

3.1155

30

9.6241e−010

3.0895

4.8305e−010

3.0944

0.9

10

1.6422e−008

 

8.2968e−009

 

15

7.0022e−009

2.1023

3.5255e−009

2.1108

20

2.8117e−009

3.1717

1.4117e−009

3.1814

25

1.3969e−009

3.1349

7.0140e−010

3.1346

30

7.9379e−010

3.1000

3.9823e−010

3.1047