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Theory and Modern Applications

Table 1 Errors and corresponding observation orders at \(t=1\), \(\alpha =1.2\)

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

λ

h = τ

\(\gamma _{3}=-0.065\)

\(\gamma _{3}=0\)

\(\gamma _{3}=0.046\)

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

Order

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

Order

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

Order

1/50

1/10

1.3091e−03

 

8.9048e−03

 

1.5872e−02

 

1/20

3.4456e−04

1.9257

2.2077e−03

2.0120

3.9986e−03

1.9889

1/40

8.8261e−05

1.9649

5.4891e−04

2.0079

9.9862e−04

2.0015

1/80

2.2181e−05

1.9925

1.3688e−04

2.0037

2.4933e−04

2.0019

0

1/10

5.4687e−03

 

1.3477e−02

 

1.9237e−02

 

1/20

1.2413e−03

2.1393

3.2862e−03

2.0360

4.7459e−03

2.0191

1/40

2.9794e−04

2.0588

8.1182e−04

2.0172

1.1770e−03

2.0116

1/80

7.3348e−05

2.0222

2.0193e−04

2.0073

2.9313e−04

2.0055

2

1/10

3.9639e−03

 

8.1213e−03

 

1.0887e−02

 

1/20

9.7650e−04

2.0212

2.1455e−03

1.9204

2.9861e−03

1.8663

1/40

2.4398e−04

2.0009

5.4410e−04

1.9794

7.6695e−04

1.9611

1/80

6.1112e−05

1.9972

1.3648e−04

1.9952

1.9300e−04

1.9905