Convergence and Stability in Collocation Methods of Equation 𝑢^′(𝑡)=𝑎𝑢(𝑡)+𝑏𝑢([𝑡])

Table 4

The absolute values of absolute errors of 𝑢_ℎ for example (7.2) with 𝑚=3.

𝑁	Gauss	Radau IIA	Lobatto IIIA	(1/3,1/2,2/3)	(1/4,1/3,1/2)	(1/2,2/3,1)
2^1	4.8459𝑒−02	9.0087𝑒−01	9.0789𝑒−01	9.0508𝑒−01	7.4280𝑒−02	9.1693𝑒−01
2^2	7.0515𝑒−03	5.0901𝑒−02	2.3033𝑒−01	8.2874𝑒−02	2.5303𝑒−02	8.3086𝑒−02
2^3	9.4311𝑒−05	1.3131𝑒−03	8.9360𝑒−03	9.9825𝑒−03	1.2122𝑒−02	6.3787𝑒−02
2^4	1.4090𝑒−06	3.5203𝑒−05	5.0981𝑒−04	6.1535𝑒−04	2.2659𝑒−03	7.4707𝑒−03
2^5	2.1766𝑒−08	1.0294𝑒−06	3.1272𝑒−05	3.8124𝑒−05	3.4308𝑒−04	7.9289𝑒−04
2^6	3.3592𝑒−10	3.1217𝑒−08	1.9458𝑒−06	2.3768𝑒−06	4.7157𝑒−05	9.0681𝑒−05
Ratio	6.4794𝑒+01	3.2977𝑒+01	1.6071𝑒+01	1.6040𝑒+01	7.2752𝑒+00	8.7437𝑒+00