Research Article
An Algorithm: Optimal Homotopy Asymptotic Method for Solutions of Systems of Second-Order Boundary Value Problems
Table 1
Absolute errors of 2nd-order solutions of
for different choices of
and also comparison with the 9th-order HPM solutions.
| | Exact | | | | HPM [3] | 1st choice | 2nd choice | 3rd choice |
| | 0.1 | −0.099 | 8.5 × 10−6 | 0.0 | 6.30503 × 10−6 | 4.48845 × 10−6 | | 0.2 | −0.192 | 1.6 × 10−5 | 0.0 | 1.41177 × 10−5 | 8.36115 × 10−7 | | 0.3 | −0.273 | 2.3 × 10−5 | 0.0 | 2.33804 × 10−5 | 1.10537 × 10−5 | | 0.4 | −0.336 | 2.9 × 10−5 | 0.0 | 3.22826 × 10−5 | 2.97367 × 10−5 | | 0.5 | −0.375 | 3.3 × 10−5 | 0.0 | 3.81526 × 10−5 | 5.6901 × 10−5 | | 0.6 | −0.384 | 3.4 × 10−5 | 0.0 | 3.86649 × 10−5 | 9.75798 × 10−5 | | 0.7 | −0.357 | 3.3 × 10−5 | 0.0 | 3.41025 × 10−5 | 1.54265 × 10−4 | | 0.8 | −0.288 | 2.7 × 10−5 | 0.0 | 2.51968 × 10−5 | 2.12191 × 10−4 | | 0.9 | −0.171 | 1.6 × 10−5 | 0.0 | 1.38339 × 10−5 | 2.11514 × 10−4 |
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