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Theory and Modern Applications

Table 6 Errors and corresponding observation orders at \(t=1\), \(\lambda =0\)

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

1.1101e−02

 

1.2168e−02

1/20

2.5816e−03

2.1044

1.8096e−02

1/40

6.0446e−04

2.0945

4.2744e−02

1/80

1.4554e−04

2.0542

1.8408e−01

1.4

−0.093

−0.09

1/10

6.5309e−03

 

1.3104e−02

1/20

1.4729e−03

2.1486

1.7784e−02

1/40

3.4402e−04

2.0981

5.3040e−02

1/80

8.3284e−05

2.0464

4.2120e−01

1.6

−0.1

−0.062

1/10

3.9390e−03

 

1.2168e−02

1/20

9.5249e−04

2.0481

1.9344e−02

1/40

2.3672e−04

2.0085

4.6176e−02

1/80

5.9105e−05

2.0018

1.8627e−01

1.8

−0.055

−0.009

1/10

4.6667e−03

 

1.1856e−02

1/20

1.1555e−03

2.0139

2.0592e−02

1/40

2.8821e−04

2.0033

4.2432e−02

1/80

7.2014e−05

2.0008

1.9375e−01