Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments

Table 2

One-leg 𝜃-methods for problem (5.1).

𝑚	𝜃=0		𝜃=1/2		𝜃=1
	AE	RE	AE	RE	AE	RE
3	1.8930𝐸−3	6.5172𝐸−1	1.4260𝐸−4	4.9094𝐸−2	3.0508𝐸−3	1.0503𝐸+000
5	1.2740𝐸−3	4.3861𝐸−1	5.1570𝐸−5	1.7754𝐸−2	1.6936𝐸−3	5.8308𝐸−1
10	6.8950𝐸−4	2.3738𝐸−1	1.2917𝐸−5	4.4470𝐸−3	7.9471𝐸−4	2.7360𝐸−1
20	3.5792𝐸−4	1.2322𝐸−1	3.2307𝐸−6	1.1123𝐸−3	3.8424𝐸−4	1.3229𝐸−1
50	1.4633𝐸−4	5.0378𝐸−2	5.1699𝐸−7	1.7799𝐸−4	1.5054𝐸−4	5.1828𝐸−2
100	7.3691𝐸−5	2.5370𝐸−2	1.2925𝐸−7	4.4498𝐸−5	7.4744𝐸−5	2.5733𝐸−2
Ratio	1.9857	1.9857	3.9999	4.0000	2.0141	2.0141