Generalization of the bisection method and its applications in nonlinear equations

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 4 Calculations of \(k_{i}\) and \(f(k_{i})\) for \(i=1,2,3\) and different values of q using QBM

q	\(k_{1}\)	\(f(k_{1})\)	\(k_{2}\)	\(f(k_{2})\)	\(k_{3}\)	\(f(k_{3})\)
0.1	0.090909091	−0.014624	0.173553719	−0.019766	0.248685199	−0.019134
0.2	0.166666667	−0.019590	0.305555556	−0.015948	0.421296296	−0.003921
0.25	0.200000000	−0.020059	0.360000000	−0.011106	0.488000000	0.005581
0.3	0.230769231	−0.019683	0.408284024	−0.005582	0.544833864	0.014771
0.4	0.285714286	−0.017295	0.489795918	0.005858	0.344023324	−0.012691
0.5	0.333333333	−0.013677	0.5555555561	0.016599	0.407407407	−0.005691
0.528	0.345549738	−0.012545	0.571694855	0.019399	0.423694124	−0.003607
0.55	0.354838710	−0.011632	0.583766909	0.021530	0.436071297	−0.001953
0.6	0.375000000	−0.009504	0.609375000	0.026147	0.462890625	0.001824
0.65	0.393939394	−0.007332	0.632690542	0.030452	0.487992876	0.005580
0.7	0.411764706	−0.005144	0.653979239	0.034459	0.511500102	0.009274
0.8	0.444444444	−0.000802	0.691358025	0.041643	0.554183813	0.016364
0.819	0.450247389	0.000011	0.202722711	−0.020056	0.314170051	−0.015291
0.9	0.473684211	0.003414	0.224376731	−0.019821	0.342469748	−0.012838
0.99	0.497487437	0.007052	0.247493750	−0.019177	0.371862469	−0.009848
1	0.5	0.007447	0.25	−0.019084	3.375	−0.009504