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Theory and Modern Applications

Table 1 Numerical accuracy of scheme (3.5) with \(M=1000\), \(\alpha =0.3\)

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

 

N

\(L^{2}\)-error

Order

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

Order

\(P^{0}\)

5

4.743511647465447e−01

–

5.230485703724679e−01

–

10

2.453322326385340e−01

0.95

2.745599439848157e−01

0.92

15

1.653406665596814e−01

0.97

1.860855920209763e−01

0.95

20

1.242678198594019e−01

0.99

1.415701279740494e−01

0.95

\(P^{1}\)

5

7.256517536855258e−02

–

9.635412347824566e−02

–

10

1.873884491779974e−02

1.95

2.552822346426505e−02

1.91

15

8.432294834666999e−03

1.97

1.166039812718010e−02

1.93

20

4.766101927280031e−03

1.98

6.630816791277043e−03

1.96

\(P^{2}\)

5

1.097532348354286e−02

–

2.164416564453414e−02

–

10

1.477316800540677e−03

2.89

2.900434572823438e−03

2.90

15

4.535585735151620e−04

2.91

8.863974464363477e−04

2.92

20

1.956222641594544e−04

2.92

3.793487019026590e−04

2.95