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Theory and Modern Applications

Table 8 The error of the third test

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

 

t

h

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

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

Er(y(t))

Hybrid Method

1

0.001

1.22665E-10

1.44872E-10

2.37014E-9

3

0.001

8.34595E-8

2.85294E-7

8.03989E-7

1

0.0001

1.63203E-13

2.12274E-13

2.45715E-12

3

0.0001

1.02396E-10

3.50464E-10

9.74921E-10

One-Leg Hybrid Method

1

0.001

3.66007E-8

9.76405E-8

6.03067E-7

3

0.001

1.38646E-7

2.52238E-7

3.53319E-6

1

0.0001

3.62941E-10

9.81447E-10

5.9809E-9

3

0.0001

3.0906E-10

1.16064E-9

2.49718E-8

Class1

1

0.001

5.5670E-6

6.86347E-6

3.45989E-5

3

0.001

3.41734E-5

1.18007E-4

2.28748E-4

1

0.0001

8.08261E-8

9.76428E-8

4.405E-7

3

0.0001

3.46347E-7

1.19601E-6

2.32459E-6

One-Leg Class1

1

0.001

6.7857E-9

1.47176E-8

1.12592E-7

3

0.001

1.69542E-7

5.4232E-7

1.85398E-6

1

0.0001

2.48221E-7

1.85705E-7

7.07125E-8

3

0.0001

3.66093E-9

1.22613E-8

3.38426E-8

HBDF

1

0.001

5.68471E-10

1.28144E-9

6.63956E-9

3

0.001

1.07333E-8

4.18462E-8

8.94225E-8

1

0.0001

7.12319E-13

1.52255E-12

6.35358E-12

3

0.0001

1.43312E-11

5.25517E-11

1.13875E-10