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Theory and Modern Applications

Table 2 Numerical accuracy of scheme (3.5) with \(M=1000\), \(\alpha =0.7\)

From: Numerical approximation of time-fractional Burgers-type equation

 

N

\(L^{2}\)-error

Order

\(L^{\infty }\)-error

Order

\(P^{0}\)

5

4.348211568435824e−01

–

5.042185301727834e−01

–

10

2.424520324538541e−01

0.95

2.624532134506741e−01

0.92

15

1.352400215461305e−01

0.97

1.589644242186741e−01

0.95

20

1.121874628534372e−01

0.99

1.289403452797642e−01

0.95

\(P^{1}\)

5

7.684216542820121e−02

–

9.154712784824911e−02

–

10

1.687534622310582e−02

1.95

2.164722782426461e−02

1.91

15

8.534804436315641e−03

1.97

1.247106712856485e−02

1.93

20

4.521403201237941e−03

1.98

6.503791571074942e−03

1.96

\(P^{2}\)

5

1.164727942789012e−02

–

2.237484026942101e−02

–

10

1.348554214954641e−03

2.89

2.899243648502348e−03

2.90

15

4.054195123465723e−04

2.91

8.057494485268102e−04

2.92

20

1.264756425642313e−04

2.92

3.752416915626942e−04

2.95