A New Class of Halley’s Method with Third-Order Convergence for Solving Nonlinear Equations

Table 6

Computational order of convergence , depending on the initial point , for the test functions and

	FG	CC	K	Bi	H2	H3	H4	H5
Order	5	6	6	8	3	3	3	3
	Test function
0.3	4.7429				2.7409	2.9318	2.9590	2.9646
0.1	4.4570	5.5455			2.8581	2.8189	2.9024	2.9244
-0.1	4.1773	5.1588	5.3015		2.9200	2.6343	2.8233	2.8702
-0.5	3.6627	4.5867	5.0169		2.9484	2.6780	2.6113	2.7280
-1	3.1506	3.1506	4.5190		2.9478	2.6982	2.4953	2.5142
-1.5	2.7697	3.5023	4.0880		2.9506	2.6627	2.5207	2.3521
-3	2.1047	2.6112	3.1698		2.8010	2.9378	2.9798	3.0175
-5	1.7092	2.0453	2.4891	4.2421	2.9347	2.7374	2.9153	2.9550
	Test function
5	4.7039
7.7	4.1354	5.1086			4.3965
8	4.0734	5.0409	5.3487		4.3498	5.3500
9	3.8739	4.8198			4.1957	5.1853
10	3.6876	4.6082	5.0228		4.0462	5.0228
12	3.3575	4.2215	4.7103		3.7670	4.7103	5.6757
15	2.9606	3.7360	4.2876		3.4044	4.2876	5.2065	6.1486
20	2.4971	3.1381	3.7147	6.1980	2.9369	3.7147	4.5447	5.4116
30	1.9836	2.4324	2.9473	4.9999	4.6232	2.9473	3.6126	4.3288
45	1.6030	1.9258	2.3177	3.9373	4.1916	2.3177	2.8057	3.3488