An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Table 4

Convergence order for Frank-Kamenetzkii problem for 𝑘=1, 𝜆=1 and different values of 𝑁.

Iter.	𝑁
	50	100	150
𝑆0
1	0.114557	0.114557	0.114557
2	0.00125407	0.00125407	0.00125407
3	1.58064𝑒−7	1.58064𝑒−7	1.58064𝑒−7
4	2.48121𝑒−15	2.48121𝑒−15	2.48121𝑒−15
5	6.09322𝑒−31	6.09322𝑒−31	6.09322𝑒−31
Rate	2.52799	2.52799	2.52799
	1.98883	1.98883	1.98883
	2.00133	2.00133	2.00133
𝑆1
1	0.0329952	0.0329952	0.0329952
2	7.69119𝑒−7	7.69119𝑒−7	7.69119𝑒−7
3	8.94424𝑒−21	8.94424𝑒−21	8.94424𝑒−21
4	9.38343𝑒−52	1.39988𝑒−62	1.39988𝑒−62
Rate	3.51966	3.51966	3.51966
	3.008	3.008	3.008
𝑆2
1	0.00877215	0.00877215	0.00877215
2	2.38344𝑒−11	2.38344𝑒−11	2.38344𝑒−11
3	1.25899𝑒−45	1.25899𝑒−45	1.25899𝑒−45
Rate	4.52861	4.52861	4.52861
𝑆3
1	0.00237755	0.00237755	0.00237755
2	6.27393𝑒−17	6.27393𝑒−17	6.27393𝑒−17
3	9.38343𝑒−52	7.50684𝑒−85	7.50684𝑒−85
Rate	5.52316	5.52316	5.52316