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

Table 1

Linear 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	1.9237𝐸−4	6.6228𝐸−2	3.0508𝐸−3	1.0503𝐸−0
5	1.2740𝐸−3	4.3861𝐸−1	6.9633𝐸−5	2.3973𝐸−2	1.6936𝐸−3	5.8308𝐸−1
10	6.8950𝐸−4	2.3738𝐸−1	1.7448𝐸−5	6.0071𝐸−3	7.9471𝐸−4	2.7360𝐸−1
20	3.5792𝐸−4	1.2322𝐸−1	4.3646𝐸−6	1.5026𝐸−3	3.8424𝐸−4	1.3229𝐸−1
50	1.4633𝐸−4	5.0378𝐸−2	6.9845𝐸−7	2.4046𝐸−4	1.5054𝐸−4	5.1828𝐸−2
100	7.3691𝐸−5	2.5370𝐸−2	1.7462𝐸−7	6.0117𝐸−5	7.4744𝐸−5	2.5733𝐸−2
Ratio	1.9857	1.9857	3.9998	3.9999	2.0141	2.0141