An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Table 2

Convergence order for Bratu problem for 𝜆=3 and different values of 𝑁.

Iter.	𝑁
	50	100	150
𝑆0
1	0.0458144	0.045864	0.045873
2	0.000954118	0.000955184	0.000955377
3	4.40809𝑒−7	4.41304𝑒−7	4.41393𝑒−7
4	9.41641𝑒−14	9.42698𝑒−14	9.4289𝑒−14
5	4.29662𝑒−27	4.30146𝑒−27	4.30234𝑒−27
Rate	1.80854	1.80867	1.80869
	1.98368	1.98369	1.98369
	1.9999	1.9999	1.9999
𝑆1
1	0.0104901	0.0105016	0.0105037
2	5.27186𝑒−7	5.27777𝑒−7	5.27884𝑒−7
3	6.88292𝑒−20	6.89065𝑒−20	6.89205𝑒−20
4	1.80799𝑒−32	1.53308𝑒−58	1.503335𝑒−58
Rate	2.73823	2.73837	2.73839
	2.99715	2.99716	2.99716
𝑆2
1	0.00253291	0.0025357	0.00253621
2	1.86441𝑒−11	1.86651𝑒−11	1.86688𝑒−11
3	1.80799𝑒−32	5.50708𝑒−44	5.5082𝑒−44
Rate	3.71869	3.71882	3.71885
𝑆3
1	0.000618859	0.000619541	0.000619664
2	4.0232𝑒−17	4.02771𝑒−17	4.02853𝑒−17
3	1.80799𝑒−32	4.68𝑒−63	4.65698𝑒−83
Rate	4.71115	4.71128	4.7113