Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method

Table 1

A comparison table for the speed of convergence of iterative methods.

Iter.	New	S	Picard-S	Vatan	Thakur-New	M	M
1	5.000000	5.000000	5.000000	5.000000	5.000000	5.000000	5.000000
2	3.410995	4.567208	4.158387	4.013700	4.158384	4.058541	4.073272
3	2.064573	4.143397	3.358521	3.090238	3.358514	3.172745	3.199868
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
10	1.000000	1.449346	1.000866	1.000098	1.000866	1.000196	1.000234
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
15	1.000000	1.046473	1.000003	1.000000	1.000003	1.000000	1.000001
16	1.000000	1.023580	1.000001	1.000000	1.000001	1.000000	1.000000
17	1.000000	1.011771	1.000000	1.000000	1.000000	1.000000	1.000000
18	1.000000	1.005826	1.000000	1.000000	1.000000	1.000000	1.000000
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
32	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000	1.000000