An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

Table 3

Iterative convergence for different schemes for the critical value of 𝜆_𝑐 for Bratu problem, 𝑁=200.

	Iter.
	𝑆0	𝑆1	𝑆2
Critical 𝜆𝑐
0	2.94303552937154	2.94303552937154	2.94303552937154
5	3.63644753861909	3.51376131743441	3.95335426360815
10	3.51383579457353	3.51383064747221	3.51383072002551
15	3.5138308350082	3.5138307190047	3.51383071919088
Absolute errors
0	0.570795189753462	0.570795189753462	0.570795189753462
5	0.122616819494092	6.94016905877781𝑒−005	0.439523544483147
10	5.07544853212138𝑒−006	7.16527859268012𝑒−008	9.00510332968452𝑒−010
15	1.15883229678815𝑒−007	1.20208731857474𝑒−010	6.58797461028371𝑒−011