Advances in Continuous and Discrete Models

Theory and Modern Applications

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°	86.1^o	81.6^o	75.2^o

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