Research Article
An Algorithm: Optimal Homotopy Asymptotic Method for Solutions of Systems of Second-Order Boundary Value Problems
Table 2
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 | −0.09 | 3.9 × 10−5 | 0.0 | 2.73481 × 10−5 | 7.24002 × 10−5 | | 0.2 | −0.16 | 7.8 × 10−5 | 0.0 | 5.22651 × 10−5 | 1.29739 × 10−4 | | 0.3 | −0.21 | 1.2 × 10−4 | 0.0 | 7.06381 × 10−5 | 1.60122 × 10−4 | | 0.4 | −0.24 | 1.6 × 10−4 | 0.0 | 7.68443 × 10−5 | 1.56816 × 10−4 | | 0.5 | −0.25 | 2.0 × 10−4 | 0.0 | 6.63508 × 10−5 | 1.20279 × 10−4 | | 0.6 | −0.24 | 2.4 × 10−4 | 0.0 | 4.01111 × 10−5 | 5.953 × 10−5 | | 0.7 | −0.21 | 2.7 × 10−4 | 0.0 | 8.66203 × 10−6 | 7.8516 × 10−6 | | 0.8 | −0.16 | 2.9 × 10−4 | 0.0 | 8.7425 × 10−6 | 5.7654 × 10−5 | | 0.9 | −0.09 | 2.4 × 10−4 | 0.0 | 1.01876 × 10−6 | 6.30638 × 10−5 |
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