Numerical Solutions of Fifth and Sixth Order Nonlinear Boundary Value Problems by Daftardar Jafari Method

Table 3

Sixth order nonlinear boundary value problem (Example 3).

𝑥	Analytic solution	Error (ADM)	Error (VIM)	Error (ITM)	Error (HPM)	Error (DJM)
0.0	1.00000	0.000	0.000	0.000	0.000	0.000
0.1	1.10517	−1.2𝐸−4	−1.2𝐸−4	−1.2𝐸−4	−1.2𝐸−4	−4.8𝐸−11
0.2	1.2214	−2.3𝐸−4	−2.3𝐸−4	−2.3𝐸−4	−2.3𝐸−4	−9.1𝐸−11
0.3	1.34986	−3.2𝐸−4	−3.2𝐸−4	−3.2𝐸−4	−3.2𝐸−4	−1.3𝐸−10
0.4	1.49182	−3.8𝐸−4	−3.8𝐸−4	−3.8𝐸−4	−3.8𝐸−4	−1.5𝐸−10
0.5	1.64872	−4.0𝐸−4	−4.0𝐸−4	−4.0𝐸−4	−4.0𝐸−4	−1.6𝐸−10
0.6	1.82212	−3.9𝐸−4	−3.9𝐸−4	−3.9𝐸−4	−3.9𝐸−4	−1.6𝐸−10
0.7	2.01375	−3.3𝐸−4	−3.3𝐸−4	−3.3𝐸−4	−3.3𝐸−4	−1.4𝐸−10
0.8	2.22554	−2.4𝐸−4	−2.4𝐸−4	−2.4𝐸−4	−2.4𝐸−4	−9.9𝐸−11
0.9	2.4596	−1.2𝐸−4	−1.2𝐸−4	−1.2𝐸−4	−1.2𝐸−4	−5.2𝐸−11
1.0	2.71828	+2.0𝐸−9	+2.0𝐸−9	+2.0𝐸−9	+2.0𝐸−9	+1.9𝐸−12

Error: analytic—numerical.