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

Table 1

The absolute values of absolute errors of 𝑢_ℎ for example (7.1) with 𝑚=2.

𝑁	Gauss	Radau IIA	Lobatto IIIA	(1/4,1/2)	(1/3,2/3)	(2/3,1)
2^1	1.2551𝑒−03	3.1476𝑒−04	1.3124𝑒−03	2.9655𝑒+02	1.3113𝑒−03	9.3953𝑒−06
2^2	4.5928𝑒−06	1.4601𝑒−06	8.5094𝑒−04	1.2874𝑒−03	6.4778𝑒−05	8.1731𝑒−10
2^3	2.4209𝑒−10	7.8934𝑒−11	8.1731𝑒−10	8.5023𝑒−07	1.0324𝑒−08	9.3978𝑒−10
2^4	6.1162𝑒−12	2.8697𝑒−11	7.7079𝑒−11	5.7012𝑒−10	1.3715𝑒−10	1.8633𝑒−10
2^5	3.4588𝑒−13	4.5808𝑒−12	3.9746𝑒−11	4.1164𝑒−11	2.0163𝑒−11	4.3362𝑒−11
2^6	2.1210𝑒−14	6.2301𝑒−13	1.2117𝑒−11	7.6587𝑒−12	4.4835𝑒−12	1.1275𝑒−11
Ratio	1.6307𝑒+01	7.3526𝑒+00	3.2802𝑒+00	5.3747𝑒+00	4.4973𝑒+00	3.8460𝑒+00