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Theory and Modern Applications

Table 6 The \(L_{\infty }\), \(L_{2}\) errors and spatial 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

1.0108e−010

 

5.1355e−011

 

15

1.9032e−011

4.1182

9.6538e−012

4.1222

20

5.8315e−012

4.1116

2.9495e−012

4.1216

25

2.3158e−012

4.1387

1.1712e−012

4.1391

30

1.0943e−012

4.1116

5.5294e−013

4.1165

0.3

10

6.2460e−010

 

3.1615e−010

 

15

1.1838e−010

4.1020

5.9811e−011

4.1065

20

3.6337e−011

4.1054

1.8305e−011

4.1157

25

1.4413e−011

4.1440

7.2600e−012

4.1444

30

6.8278e−012

4.0979

3.4357e−012

4.1035

0.5

10

1.5276e−009

 

7.7139e−010

 

15

2.9494e−010

4.0563

1.4869e−010

4.0604

20

9.1714e−011

4.0604

4.6102e−011

4.0705

25

3.6693e−011

4.1054

1.8444e−011

4.1055

30

1.7524e−011

4.0534

8.8006e−012

4.0583

0.7

10

2.5752e−009

 

1.2990e−009

 

15

5.0324e−010

4.0265

2.5347e−010

4.0302

20

1.5761e−010

4.0355

7.9159e−011

4.0454

25

6.3275e−011

4.0899

3.1783e−011

4.0894

30

3.0340e−011

4.0315

1.5226e−011

4.0364

0.9

10

2.1167e−009

 

1.0673e−009

 

15

4.1447e−010

4.0216

2.0867e−010

4.0253

20

1.2990e−010

4.0330

6.5219e−011

4.0427

25

5.2071e−011

4.0967

2.6146e−011

4.0963

30

2.4980e−011

4.0288

1.2532e−011

4.0336