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Theory and Modern Applications

Table 4 Errors and corresponding observation orders at \(t=1\), \(\lambda =1/50\)

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

α

\(\beta _{3}\)

\(\gamma _{3}\)

h = τ

CN-TWSGD

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

Order

CPU time

1.2

−0.042

−0.065

1/10

4.6812e−03

 

1.2119e−02

1/20

1.1156e−03

2.0691

2.1528e−02

1/40

2.6920e−04

2.0511

4.9296e−02

1/80

6.6095e−05

2.0261

1.8533e−01

1.4

−0.093

−0.09

1/10

3.5917e−03

 

1.1856e−02

1/20

8.0067e−04

2.1654

1.9344e−02

1/40

1.8738e−04

2.0952

5.0544e−02

1/80

4.5523e−05

2.0413

1.9469e−01

1.6

−0.1

−0.062

1/10

2.8683e−03

 

1.5912e−02

1/20

6.8778e−04

2.0602

1.7784e−02

1/40

1.7060e−04

2.0113

4.4928e−02

1/80

4.2575e−05

2.0025

1.8221e−01

1.8

−0.055

−0.009

1/10

4.2551e−03

 

1.3104e−02

1/20

1.0522e−03

2.0158

1.8408e−02

1/40

2.6237e−04

2.0037

4.4304e−02

1/80

6.5551e−05

2.0009

1.9531e−01