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

Table 3

Numerical solutions and errors of AB3, LMM1 and LMM2 for (5.1).

𝑡𝑛	𝑌(𝑡𝑛)	𝑌𝑛(AB3)	𝐸𝑛(AB3)	𝑌𝑛(LMM1)	𝐸𝑛(LMM1)	𝑌𝑛(LMM2)	𝐸𝑛(LMM2)
		ℎ=0.0001		ℎ=0.004		ℎ=0.01
	0.7981	0.7803	−0.0178	0.7981	−0.105𝐸−4	0.7957	−0.241𝐸−2
0.0200	0.1627	0.1801	0.0174	0.1627	0.174𝐸−4	0.1639	0.122𝐸−2
	0.0093	0.2086	0.1993	0.0104	0.109𝐸−2	0.0079	0.145𝐸−2
	0.5595	0.5217	−0.0378	0.5595	−0.250𝐸−5	0.5593	−0.146𝐸−3
0.0400	0.3636	0.4010	0.0374	0.3636	−0.420𝐸−5	0.3643	0.709𝐸−3
	0.2077	0.2588	0.0511	0.2076	0.100𝐸−3	0.2085	0.816𝐸−3
	0.4407	0.4205	−0.0202	0.4407	0.100𝐸−5	0.4407	−0.551𝐸−4
0.0600	0.4463	0.4661	0.0198	0.4463	0.242𝐸−5	0.4463	0.550𝐸−4
	0.1282	0.1199	−0.0083	0.1280	−0.220𝐸−3	0.1282	0.854𝐸−4
	0.4045	0.3994	−0.0051	0.4045	−0.122𝐸−6	0.4045	0.214𝐸−5
0.0800	0.4476	0.4524	0.0048	0.4476	0.274𝐸−6	0.4476	0.324𝐸−5
	0.0383	0.0228	−0.0155	0.0383	−0.517𝐸−4	0.0383	−0.859𝐸−5
	0.3964	0.3972	0.800𝐸−3	0.3964	0.815𝐸−4	0.3964	0.662𝐸−5
0.1000	0.4223	0.4212	−0.100𝐸−2	0.4223	−0.512𝐸−4	0.4223	−0.160𝐸−5
	−0.0019	−0.0090	0.800𝐸−2	−0.0019	0.541𝐸−4	−0.0019	0.221𝐸−5