Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Errors of shooting techniques \(\vert \tilde{F}(s_{m}) \vert \) in (41) versus the maximum number of iterations with various values of \(s_{0}\) in Example 4.1. We set \(h=0.01\), \(\alpha _{1}=0.4\), \(\alpha _{2}=1.7\)

From: An efficient numerical approach for solving two-point fractional order nonlinear boundary value problems with Robin boundary conditions

m	Newton’s method					Halley’s method
m	\(s_{0}=0.2\)	\(s_{0}=0.4\)	\(s_{0}=0.6\)	\(s_{0}=0.8\)	\(s_{0}=1.0\)	\(s_{0}=0.2\)	\(s_{0}=0.4\)	\(s_{0}=0.6\)	\(s_{0}=0.8\)	\(s_{0}=1.0\)
1	0.604011	1.305541	2.105771	3.00776	4.017051	0.603191	1.304704	2.104838	3.006644	4.01565
2	0.042234	1.48E−01	0.303846	5.05E−01	0.753495	0.054329	1.90E−01	0.392297	6.59E−01	0.995211
3	0.000274	3.25E−03	0.01249	3.10E−02	0.061341	0.000604	6.84E−03	0.025715	6.31E−02	0.124161
4	7.31E−08	7.33E−07	2.17E−05	1.46E−04	0.000578	9.11E−08	8.24E−06	1.34E−04	0.000813	0.003036
5	2.28E−11	2.29E−10	6.71E−09	4.22E−08	1.25E−07	2.58E−11	2.32E−09	3.41E−08	8.56E−08	1.15E−06
6	7.11E−15	7.19E−14	2.10E−12	1.32E−11	3.91E−11	6.22E−15	6.55E−13	9.64E−12	2.42E−11	3.26E−10
7	0	0	8.88E−16	4.44E−15	1.07E−14	8.88E−16	0	2.66E−15	6.22E−15	9.15E−14
8	0	0	0	0	1.78E−15	8.88E−16	0	8.88E−16	0	8.88E−16
9	0	0	0	0	0	8.88E−16	0	8.88E−16	0	8.88E−16
10	0	0	0	0	0	8.88E−16	0	8.88E−16	0	8.88E−16

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