Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

Table 4

Comparison of absolute errors for Example 1 between proposed method and the method given in [13].

Proposed method						MDM—cubic B-spline collocation method [13]
𝑥	GA	IPA	ASA	GA-IPA	GA-ASA	Approach I; (with 𝑁=20)	Approach II; (with 𝑁=20)
0	2.87𝐸−05	−2.92𝐸−05	2.37𝐸−06	3.99𝐸−06	−2.13𝐸−06	1.05𝐸−05	2.00𝐸−06
0.1	3.04𝐸−05	−2.29𝐸−05	1.56𝐸−06	3.26𝐸−06	−1.36𝐸−06	1.05𝐸−05	1.99𝐸−06
0.2	3.13𝐸−05	−2.12𝐸−05	1.32𝐸−06	3.05𝐸−06	−6.17𝐸−07	1.03𝐸−05	1.97𝐸−06
0.3	2.99𝐸−05	−1.87𝐸−05	1.05𝐸−06	2.65𝐸−06	−9.22𝐸−07	1.02𝐸−05	1.94𝐸−06
0.4	2.91𝐸−05	−1.51𝐸−05	6.56𝐸−07	2.17𝐸−06	−9.39𝐸−07	9.93𝐸−06	1.83𝐸−06
0.5	2.98𝐸−05	−1.18𝐸−05	3.45𝐸−07	1.94𝐸−06	−2.89𝐸−07	9.62𝐸−06	1.78𝐸−06
0.6	3.04𝐸−05	−1.03𝐸−05	3.07𝐸−07	2.05𝐸−06	5.00𝐸−07	6.93𝐸−06	1.67𝐸−06
0.7	2.93𝐸−05	−1.07𝐸−05	4.58𝐸−07	2.17𝐸−06	8.25𝐸−07	4.75𝐸−06	1.34𝐸−06
0.8	2.62𝐸−05	−1.21𝐸−05	5.10𝐸−07	1.93𝐸−06	5.64𝐸−07	2.93𝐸−06	9.20𝐸−07
0.9	2.26𝐸−05	−1.25𝐸−05	2.92𝐸−07	1.36𝐸−06	1.29𝐸−07	1.37𝐸−06	4.57𝐸−07
1.0	2.04𝐸−05	−1.07𝐸−05	2.50𝐸−08	9.65𝐸−07	6.22𝐸−08	0	0