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Theory and Modern Applications

Table 6 The error of the first test

From: G-stability one-leg hybrid methods for solving DAEs

 

t

h

\(\operatorname{Er}(y_{1}(t))\)

\(\operatorname{Er}(y_{2}(t))\)

Hybrid Method (4)

3

0.001

4.78965E-8

1.53733E-8

6

0.001

2.07019E-6

3.41682E-7

3

0.0001

1.67133E-10

4.69775E-11

6

0.0001

1.26784E-9

1.45462E-10

One-Leg of Hybrid Method (4)

3

0.001

8.87175E-6

4.70979E-6

6

0.001

4.45514E-4

8.88051E-5

3

0.0001

8.92249E-8

4.72626E-8

6

0.0001

4.48537E-6

8.9293E-7

Hybrid Method (27)

3

0.001

1.15024E-7

3.66907E-8

6

0.001

5.31317E-6

8.72459E-7

3

0.0001

3.5984E-10

1.107355E-10

6

0.0001

1.12391E-8

1.93154E-9

One-Leg of Hybrid Method (27)

3

0.001

1.28838E-6

9.03448E-8

6

0.001

2.06502E-4

2.96481E-5

3

0.0001

1.22774E-8

1.09555E-9

6

0.0001

2.02582E-6

2.90166E-7

HBDF

3

0.001

4.67957E-9

1.52812E-8

6

0.001

7.17848E-6

1.01547E-6

3

0.0001

2.87855E-10

9.16494E-11

6

0.0001

4.06857E-8

6.55177E-9