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Theory and Modern Applications

Table 5 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

Proposed

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

Order

CPU time

1.2

−0.042

−0.065

1/10

1.3356e−03

 

1.5912e−02

1/20

3.5152e−04

1.9258

2.2152e−02

1/40

9.0044e−05

1.9649

4.8672e−02

1/80

2.2629e−05

1.9925

1.9594e−01

1.4

−0.093

−0.09

1/10

1.4612e−03

 

1.3728e−02

1/20

4.2047e−04

1.7971

1.9344e−02

1/40

1.0892e−04

1.9487

5.0856e−02

1/80

2.7456e−05

1.9881

2.0280e−01

1.6

−0.1

−0.062

1/10

2.2694e−03

 

1.2480e−02

1/20

5.0328e−04

2.1729

1.9656e−02

1/40

1.2209e−04

2.0434

5.0544e−02

1/80

3.0302e−05

2.0105

1.9313e−01

1.8

−0.055

−0.009

1/10

7.1897e−03

 

1.4664e−02

1/20

1.7878e−03

2.0077

2.2464e−02

1/40

4.4632e−04

2.0020

5.1480e−02

1/80

1.1154e−04

2.0005

2.0062e−01