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

Table 5

Comparison of methods of various orders in terms of the error in the consecutive iterations, the absolute value of the error, the absolute value of the function, and the computational order of convergence.

Order	5	6	6	8	3	3	3	3
	1.49535	1.56508	1.56508	1.68179	1.44225	1.44225	1.44225	1.44225
	Test function
	4.6e-02	2.35	1.65	3.9e-01	2.34	1.65	1.18	8.6e-01
	3.0-10	5.3-03	3.4-04	7.2-11	7.0-03	3.4-04	9.3-06	1.5-07
	2.1-09	3.7-02	2.4-3	5.1-10	4.9-02	2.4-03	6.5-05	1.0-06
	2.1929	2.7257	3.28	5.5369	2.5987	3.2800	4.0233	4.8121
	Test function
	2.0-01	1.3-01	7.3-02	2.44	1.4-01	8.6-02	5.8-02	4.3-02
	6.4-05	7.8-07	8.8-09	2.44	1.9-05	3.9-06	1.2-06	5.1-07
	1.2-04	1.4-06	1.6-08	8.1-03	3.4-05	7.0-06	2.2-06	9.0-07
	3.2053	4.0336	4.5435	2 it	3.0818	2.9867	2.8803	2.8115
	Test function
	3.5-03	1.3-02	1.5-02	1.59	8.0-02	3.5-02	7.7-03	9.6-03
	8.7-13	7.2-12	4.2-12	1.59	1.2-05	1.2-06	1.3-08	2.5-08
	3.2-12	2.6-11	1.5-11	6.3-03	4.6-05	4. 7-06	5.0-08	9.8-08
	3.1506	3.1506	4.5190	2 it	2.9478	2.6982	2.4953	2.5142
	Test function
	7.4-02	3.7-02	1.2-02	9.0-01	6.5-04	8.3-3	3.8-02	5.2-04
	5.1-06	7.0-09	5.1-13	9.0-01	9.2-11	1.9-07	1.8-05	4.5-11
	1.5-05	2.1-08	1.5-12	9.8-03	2.8-10	5.7-07	5.4-05	1.4-10
	3.8395	4.8730	5.5050	2 it	2.9923	3.0445	2.9142	2.2690
,	Test function
	1.0-01	4.7-02	1.3-02		4.9-04	3.5-03	1.2-02	4.4-02
	1.0-06	6.8-10	2.1-14		8.5-12	3.0-09	1.3-07	6.1-06
	1.9-05	9.4-09	3.0-13		1.2-10	4.2-08	1.9-06	8.5-05
	4.0505	5.0940	5.6205		2.9969	2.2657	3.0119	3.0580
	Test function
	4.3-02	2.5-01	3.9-02	1.8-01	1.9-03	1.5-03	1.6-03	1.6-03
	1.4-09	2.0-12	2.1-12	1.8-01	4.4-10	2.4-10	2.8-10	2.7-10
	2.4-09	3.3-12	3.5-12	4.06-03	7.3-10	3.9-10	4.7-10	4.8-10
	4.5893	5.4180	6.1742	2 it	3.0336	3.0313	3.0319	3.0317
,	Test function
	1.3-02	3.7-03	4.5-01	4.5-01	2.2-04	7.1-04	1.5-03	2.9-03
	1.3-09	6.7-15	4.5-01	4.5-01	5.4-12	1.8-10	1.9-09	2.9-03
	2.4-08	1.2-13	5.7-03	7.4-03	9.7-11	3.3-09	3.4-08	1.3-08
	4.5698	5.5998	2 it	2 it	2.9860	2.9815	2.9731	2.9649