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Theory and Modern Applications

Table 1 Absolute error for solving Example 1 using FAM22

From: Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict–correct technique

t

α = 0.1

α = 0.3

α = 0.5

α = 0.7

α = 0.9

N = 10

0.1

2.1237×10−2

1.6869×10−2

1.5034×10−2

1.1942×10−3

9.4858×10−5

0.2

3.4132×10−1

2.1077×10−2

1.6911×10−2

1.0716×10−3

5.5759×10−5

0.3

2.2375×10−2

1.2294×10−2

9.5737×10−3

5.5784×10−4

1.9550×10−5

0.4

8.3608×10−1

4.0257×10−2

3.0489×10−3

1.6929×10−4

4.1245×10−4

0.5

2.4287×10−1

9.9985×10−2

3.3196×10−3

1.9016×10−4

6.8290×10−5

0.6

5.9337×10−2

2.0654×10−2

1.4528×10−3

3.4112×10−4

9.4593×10−4

0.7

1.1839×10−2

3.6469×10−3

3.4620×10−4

1.1934×10−4

1.0920×10−4

0.8

2.1256×10−1

5.4729×10−3

2.5639×10−4

1.6121×10−4

9.5445×10−4

0.9

1.3815×10−2

1.0644×10−2

4.3516×10−3

1.6825×10−4

4.7081×10−4

1.0

1.4196×10−2

2.2823×10−3

2.0042×10−3

1.1475×10−3

1.1258×10−4

MXE (P)

8.9981×10−1

6.1012×10−1

2.6222×10−2

1.2265×10−3

9.3398×10−4

MXE (C)

8.3608×10−1

9.9985×10−2

1.6911×10−2

1.1942×10−3

9.4593×10−4

N = 100

0.1

1.8929×10−3

1.1275×10−3

2.2043×10−4

2.8474×10−5

1.9437×10−6

0.2

2.0568×10−4

4.1104×10−4

4.3601×10−5

5.5340×10−6

3.0493×10−6

0.3

1.2279×10−4

2.1909×10−4

1.4540×10−5

3.0654×10−5

2.9076×10−6

0.4

1.9977×10−2

1.0491×10−4

4.1222×10−4

1.0029×10−5

1.1102×10−4

0.5

2.0961×10−2

6.5845×10−5

2.9836×10−4

2.4317×10−4

2.4317×10−4

0.6

2.9182×10−3

2.5162×10−5

2.5287×10−4

4.8042×10−4

2.8421×10−4

0.7

2.4222×10−3

1.3609×10−5

2.5527×10−4

2.0413×10−4

4.7843×10−4

0.8

3.0189×10−3

1.6910×10−4

2.1368×10−4

1.1368×10−4

6.9968×10−4

0.9

2.3863×10−3

2.7373×10−3

2.6067×10−4

1.2458×10−4

8.4414×10−5

1.0

2.2487×10−4

9.1943×10−4

3.8386×10−4

5.3033×10−5

3.1828×10−5

MXE (P)

3.9876×10−2

5.1160×10−2

4.7111×10−3

8.1344×10−4

6.9879×10−4

MXE (C)

2.0961×10−2

1.1275×10−3

4.1222×10−4

4.8042×10−4

4.7843×10−4

N = 1000

0.1

2.3829×10−6

1.2597×10−6

4.1370×10−7

2.0759×10−7

4.5297×10−8

0.2

3.8739×10−5

6.2953×10−6

4.2549×10−6

4.2424×10−6

1.3459×10−6

0.3

1.7056×10−4

3.4361×10−5

2.3979×10−5

2.1452×10−6

3.7382×10−6

0.4

2.0515×10−4

1.1117×10−4

7.9413×10−5

5.1713×10−5

2.8182×10−5

0.5

3.1833×10−4

2.6778×10−5

1.9476×10−4

9.4507×10−5

3.4317×10−5

0.6

3.4375×10−4

5.2858×10−5

3.8462×10−4

1.6811×10−4

1.8441×10−5

0.7

2.0771×10−4

8.9072×10−4

6.4326×10−4

2.6662×10−4

2.7278×10−5

0.8

2.9196×10−4

1.2836×10−4

9.0151×10−4

3.5514×10−4

2.4969×10−5

0.9

1.1469×10−4

1.4765×10−4

9.5666×10−4

3.3925×10−4

6.5225×10−5

1.0

1.2166×10−4

8.2634×10−4

3.0109×10−4

4.6796×10−5

2.5072×10−6

MXE (P)

1.4329×10−3

1.0997×10−3

1.0342×10−3

4.8332×10−4

8.9883×10−5

MXE (C)

3.4375×10−4

8.9072×10−4

9.5666×10−4

3.3925×10−4

6.5225×10−5

EOC (P)

1.44

1.67

0.66

0.23

0.89

EOC(C)

1.60

1.56

1.81

1.54

1.86