Estimation of Longest Stability Interval for a Kind of Explicit Linear Multistep Methods

Table 4

Numerical solutions and errors of LMM1, BDF3, and AM3 for (5.1).

𝑡𝑛	𝑌(𝑡𝑛)	𝑌𝑛(LMM1)	𝐸𝑛(LMM1)	𝑌𝑛(BDF3)	𝐸𝑛(BDF3)	𝑌𝑛(AM3)	𝐸𝑛(AM3)
		ℎ=0.0025		ℎ=0.0025		ℎ=0.0025
	7.9808𝐸−1	7.9826𝐸−1	1.7435𝐸−4	7.9789𝐸−1	−1.9274𝐸−4	7.9778𝐸−1	−3.0096𝐸−4
0.0200	1.6271𝐸−1	1.6253𝐸−1	−1.7435𝐸−4	1.6290𝐸−1	1.9274𝐸−4	1.6301𝐸−1	3.0097𝐸−4
	9.2784𝐸−3	9.2644𝐸−3	−1.3993𝐸−5	9.3240𝐸−3	4.5652𝐸−5	9.4174𝐸−3	1.3908𝐸−4
	5.5952𝐸−1	5.5966𝐸−1	1.4495𝐸−4	5.5935𝐸−1	−1.6673𝐸−4	5.5872𝐸−1	−8.0064𝐸−4
0.0400	3.6360𝐸−1	3.6346𝐸−1	−1.4496𝐸−4	3.6377𝐸−1	1.6673𝐸−4	3.6440𝐸−1	8.0064𝐸−4
	2.0771𝐸−1	2.0798𝐸−1	2.7493𝐸−4	2.0743𝐸−1	−2.7512𝐸−4	2.0737𝐸−1	−3.3240𝐸−4
	4.4065𝐸−1	4.4065𝐸−1	1.7550𝐸−6	4.4064𝐸−1	−1.2265𝐸−5	4.3975𝐸−1	−9.0526𝐸−4
0.0600	4.4627𝐸−1	4.4627𝐸−1	−1.7579𝐸−6	4.4628𝐸−1	1.2268𝐸−5	4.4717𝐸−1	9.0527𝐸−4
	1.2817𝐸−1	1.2846𝐸−1	2.8861𝐸−4	1.2786𝐸−1	−3.0907𝐸−4	1.2702𝐸−1	−1.1478𝐸−3
	4.0454𝐸−1	4.0447𝐸−1	−6.3347𝐸−5	4.0460𝐸−1	6.3188𝐸−5	4.0382𝐸−1	−7.1785𝐸−4
0.0800	4.4761𝐸−1	4.4767𝐸−1	6.3343𝐸−5	4.4754𝐸−1	−6.3184𝐸−5	4.4833𝐸−1	7.1787𝐸−4
	3.8313𝐸−2	3.8439𝐸−2	1.2611𝐸−4	3.8170𝐸−2	−1.4361𝐸−4	3.6721𝐸−2	−1.5922𝐸−3
	3.9645𝐸−1	3.9640𝐸−1	−5.1188𝐸−5	3.9650𝐸−1	5.4584𝐸−5	3.9595𝐸−1	−5.0282𝐸−4
0.1000	4.2228𝐸−1	4.2233𝐸−1	5.1183𝐸−5	4.2223𝐸−1	−5.4580𝐸−5	4.2278𝐸−1	5.0285𝐸−4
	1.8894𝐸−3	−1.8911𝐸−3	−1.7216𝐸−6	−1.8947𝐸−3	−5.3187𝐸−6	−3.4785𝐸−3	−1.5891𝐸−3