Table 3 Comparison the approximate frequencies of Eq. (23) between the present method and the usual HBM method with the exact frequency \( \dot{\varphi }_{Ex} \), obtained by direct numerical integration
From: The rapidly convergent solutions of strongly nonlinear oscillators
a | \( \dot{\varphi }_{Ex} \) | \( \dot{\varphi }_{3(q,Usual)} \) Er (%) | \( \dot{\varphi }_{3(q,\Pr esent)} \) Er (%) |
|---|---|---|---|
1.8 | 1.52154 | 1.52669 | 1.52180 |
0.339 | 0.017 | ||
2.0 | 1.67047 | 1.68325 | 1.67091 |
0.765 | 0.026 | ||
2.2 | 1.84092 | 1.86926 | 1.84103 |
1.540 | 0.006 | ||
2.4 | 2.03064 | 2.0876 | 2.028 |
2.805 | 0.130 | ||
2.6 | 2.236 | 2.34108 | 2.22324 |
4.700 | 0.571 | ||
2.8 | 2.45251 | 2.63242 | 2.41143 |
7.336 | 1.675 |