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Theory and Modern Applications

Table 11 Errors and corresponding observation orders at \(t=1\), \(\gamma _{3}=0\)

From: Second-order numerical methods for the tempered fractional diffusion equations

α

h = τ

λ = 2

λ = 3

λ = 5

\(\|e\|_{L_{2}}\)

Order

\(\|e\|_{L_{2}}\)

Order

\(\|e\|_{L_{2}}\)

Order

1.2

1/10

4.4064e−03

 

7.3432e−03

 

1.3289e−02

 

1/20

1.4170e−03

1.6368

2.3874e−03

1.6210

4.6713e−03

1.5083

1/40

4.4624e−04

1.6669

7.1388e−04

1.7417

1.3593e−03

1.7810

1/80

1.4351e−04

1.6367

2.1251e−04

1.7482

3.7612e−04

1.8536

1.5

1/10

2.7871e−04

 

6.9236e−04

 

2.1027e−03

 

1/20

9.6202e−05

1.5346

2.3030e−04

1.5880

7.2237e−04

1.5414

1/40

3.1225e−05

1.6234

7.2323e−05

1.6710

2.3189e−04

1.6393

1/80

1.0186e−05

1.6161

2.1899e−05

1.7236

6.6164e−05

1.8093

1.8

1/10

2.6714e−04

 

2.7940e−04

 

3.2526e−04

 

1/20

3.7920e−05

2.8166

3.7952e−05

2.8801

3.9166e−05

3.0539

1/40

5.2055e−06

2.8649

5.1329e−06

2.8863

5.0821e−06

2.9461

1/80

7.0658e−07

2.8811

6.9299e−07

2.8889

6.8096e−07

2.8998