Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations

Table 1

Errors and ratio for (37).

	Euler-Maclaurin method		𝜃-methods		2-Radau IA method
	AE	RE	AE	RE	AE	RE
𝑚=2	1.5555𝐸−13	5.0586𝐸−5	2.7882𝐸−9	9.0670𝐸−1	6.5320𝐸−10	2.1240𝐸−1
𝑚=3	1.3547𝐸−14	4.4054𝐸−6	1.8944𝐸−9	6.1610𝐸−1	1.7228𝐸−10	5.6000𝐸−2
𝑚=5	6.2942𝐸−16	2.0469𝐸−7	8.6318𝐸−10	2.8070𝐸−1	3.5051𝐸−11	1.1400𝐸−2
𝑚=10	9.8172𝐸−18	3.1926𝐸−9	2.3894𝐸−10	7.7700𝐸−2	4.2380𝐸−12	1.4000𝐸−3
𝑚=20	1.5337𝐸−19	4.9876𝐸−11	6.1287𝐸−11	1.9900𝐸−2	5.2217𝐸−13	1.6981𝐸−4
𝑚=40	2.7140𝐸−21	8.8259𝐸−13	1.5420𝐸−11	5.0000𝐸−3	6.4824𝐸−14	2.1081𝐸−5
Ratio	56.5107	56.5110	3.9745	3.9800	8.0552	8.0551