An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Table 1

Convergence order and absolute error for Bratu problem for 𝜆=1 and different values of 𝑁.

Iter.	𝑁
	50	100	150	200
𝑆0
1	0.000764899	0.000765714	0.000765861	0.000765913
2	3.22437𝑒−8	3.228𝑒−8	3.22866𝑒−8	3.22889𝑒−8
3	5.67396𝑒−17	5.68041𝑒−17	5.68158𝑒−17	5.68198𝑒−17
4	1.75415𝑒−34	1.75614𝑒−34	1.7565𝑒−34	1.75663𝑒−34
5	7.71203𝑒−49	1.67808𝑒−69	1.67843𝑒−69	1.67855𝑒−69
Rate	2.03003	2.03014	2.03016	2.03017
	2.00097	2.00098	2.00098	2.00098
	2.00008	2.00008	2.00008	2.00008
𝑆1
1	0.000010196	0.0000102072	0.0000102092	0.0000102099
2	6.3566𝑒−18	6.36381𝑒−18	6.36511𝑒−18	6.36557𝑒−18
3	7.71203𝑒−49	1.52735𝑒−54	1.52766𝑒−54	1.52777𝑒−54
4	7.71203𝑒−49	1.14254𝑒−95	3.04915𝑒−142	2.11033𝑒−164
Rate	3.02829	3.0284	3.02842	3.02842
	2.53302	3.00035	3.00035	3.00035
𝑆2
1	1.35077𝑒−7	1.35226𝑒−7	1.35253𝑒−7	1.35262𝑒−7
2	2.18092𝑒−31	2.1834𝑒−31	2.18384𝑒−31	2.184𝑒−31
3	7.71203𝑒−49	1.1425376𝑒−95	1.46619𝑒−126	1.46629𝑒−126
Rate	4.02691	4.02701	4.02702	4.02703
𝑆3
1	1.7892𝑒−9	1.79116𝑒−9	1.79152𝑒−9	1.79164𝑒−9
2	1.79244𝑒−48	1.31437𝑒−48	1.31464𝑒−48	1.31473𝑒−48
3	7.71203𝑒−49	1.14254𝑒−95	3.04915𝑒−142	1.03327𝑒−188
Rate	5.00878	5.02624	5.02626	5.02627