Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Errors of shooting techniques \(\vert \tilde{F}(s_{m}) \vert \) in (41) versus the maximum number of iterations m for each \(s_{0}\) in Example 4.2 as we set \(\alpha _{1} = 0.4\), \(\alpha _{2}=1.7\), \(h=0.01\)

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	0.414113	0.890547	1.42639	2.02066	2.674035	0.414046	0.890413	1.426145	2.020256	2.673415
2	0.027748	9.51E−02	0.190648	3.11E−01	0.456212	0.03142	1.08E−01	0.219523	3.66E−01	0.549419
3	0.000177	1.93E−03	0.007068	1.70E−02	0.032652	0.000258	2.80E−03	0.010391	2.54E−02	0.050225
4	1.51E−08	9.56E−07	1.20E−05	6.71E−05	0.000243	1.61E−08	2.10E−06	2.89E−05	1.70E−04	0.000646
5	6.59E−13	4.20E−11	5.57E−10	3.99E−09	2.45E−08	1.25E−13	1.52E−11	1.33E−12	6.56E−09	1.08E−07
6	0	1.89E−15	2.44E−14	1.75E−13	1.07E−12	5.55E−17	1.67E−16	1.11E−16	5.11E−14	8.40E−13
7	0	0	0	0	1.67E−16	5.55E−17	5.55E−17	5.55E−17	5.55E−17	5.55E−17
8	0	0	0	0	5.55E−17	5.55E−17	5.55E−17	5.55E−17	5.55E−17	0
9	0	0	0	0	0	5.55E−17	5.55E−17	5.55E−17	5.55E−17	0
10	0	0	0	0	0	5.55E−17	5.55E−17	5.55E−17	5.55E−17	0

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