Table 7 Comparison of absolute errors of approximated solutions utilizing approach III for \(\lambda =0.5\) and \(\lambda =1\)
From: Three new approaches for solving a class of strongly nonlinear two-point boundary value problems
x | M = 4 | M = 5 | MHPT [4] | LT-MDM [11] |
|---|---|---|---|---|
λ = 0.5 | ||||
0.1 | 3.7 × 10−9 | 4.4 × 10−13 | 8.2 × 10−4 | 7.7 × 10−4 |
0.2 | 2.2 × 10−8 | 5.8 × 10−12 | 1.6 × 10−3 | 1.5 × 10−3 |
0.3 | 1.9 × 10−8 | 1.6 × 10−12 | 2.3 × 10−3 | 2.1 × 10−3 |
0.4 | 4.1 × 10−8 | 8.8 × 10−12 | 2.9 × 10−3 | 2.7 × 10−3 |
0.5 | 9.6 × 10−7 | 7.0 × 10−12 | 3.2 × 10−3 | 3.0 × 10−3 |
0.6 | 7.5 × 10−7 | 6.1 × 10−12 | 3.4 × 10−3 | 3.1 × 10−3 |
0.7 | 3.9 × 10−8 | 4.5 × 10−12 | 3.2 × 10−3 | 3.0 × 10−3 |
0.8 | 6.4 × 10−8 | 3.7 × 10−12 | 2.7 × 10−3 | 2.4 × 10−3 |
0.9 | 3.0 × 10−8 | 2.9 × 10−13 | 1.6 × 10−3 | 1.5 × 10−3 |
λ = 1 | ||||
0.1 | 1.2 × 10−8 | 1.4 × 10−12 | 3.6 × 10−3 | 2.9 × 10−3 |
0.2 | 5.3 × 10−86 | 8.3 × 10−11 | 7.1 × 10−2 | 5.9 × 10−3 |
0.3 | 1.8 × 10−9 | 2.9 × 10−11 | 1.0 × 10−2 | 8.2 × 10−3 |
0.4 | 9.7 × 10−8 | 5.0 × 10−11 | 1.3 × 10−2 | 1.0 × 10−2 |
0.5 | 4.0 × 10−8 | 5.7 × 10−11 | 1.6 × 10−2 | 1.2 × 10−2 |
0.6 | 2.6 × 10−8 | 3.3 × 10−11 | 1.7 × 10−2 | 1.3 × 10−2 |
0.7 | 8.5 × 10−7 | 6.1 × 10−11 | 1.7 × 10−2 | 1.3 × 10−2 |
0.8 | 7.7 × 10−7 | 4.3 × 10−12 | 1.5 × 10−2 | 1.1 × 10−2 |
0.9 | 1.3 × 10−8 | 7.4 × 10−12 | 9.7 × 10−3 | 7.4 × 10−3 |