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Theory and Modern Applications

Table 7 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

Proposed

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

Order

CPU time

1.2

−0.042

−0.065

1/10

5.4687e−03

 

1.3728e−02

1/20

1.2413e−03

2.1393

2.2152e−02

1/40

2.9794e−04

2.0588

4.9608e−02

1/80

7.3348e−05

2.0222

1.9594e−01

1.4

−0.093

−0.09

1/10

1.4523e−03

 

1.3728e−02

1/20

2.8548e−04

2.3468

2.2776e−02

1/40

6.7785e−05

2.0744

4.8048e−02

1/80

1.6770e−05

2.0151

1.8876e−01

1.6

−0.1

−0.062

1/10

3.3311e−03

 

1.3104e−02

1/20

7.7293e−04

2.1076

1.9968e−02

1/40

1.8976e−04

2.0262

4.5240e−02

1/80

4.7234e−05

2.0063

1.9656e−01

1.8

−0.055

−0.009

1/10

7.5583e−03

 

1.4976e−02

1/20

1.8800e−03

2.0073

2.0904e−02

1/40

4.6938e−04

2.0019

4.8048e−02

1/80

1.1730e−04

2.0006

1.8970e−01