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Table 5 A(α)-stability for BDF, EBDF, A-EBDF, MEBDF, Enright methods, HEBDF, and The class (3–4) for various orders

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

k 1 2 3 4 5 6 7
BDF  
 Order 1 2 3 4 5 6 -
α 90° 90° 88° 73° 51° 18° -
EBDF  
 Order 2 3 4 5 6 7 8
α 90° 90° 90° 87.61° 80.2° 67.7° 48.8°
A-EBDF  
 Order 2 3 4 5 6 7 8
α 90° 90° 90° 88.85° 84.2° 75° 61°
MEBDF  
 Order 2 3 4 5 6 7 8
α 90° 90° 90° 88.4° 82.5° 74.5° 62°
Enright methods  
 Order 3 4 5 6 7 8 9
α 90° 90° 87.88° 82.03° 73.10° 59.95° 37.61°
HEBDF  
 Order 2 3 4 5 6 7 8
α 90° 90° 90° 89.013° 85.2° 77.195° 60.686°
The class (3–4)  
 Order 2 3 4 5 6 7 8
α 90° 90° 90° 90° 86.1o 81.6o 75.2o