Research Article
Approximate Periodic Solution for the Nonlinear Helmholtz-Duffing Oscillator via Analytical Approaches
Table 3
Comparison between MMA, FHA, SHA, FGEM, and SGEM results with exact ones and HPM responses (
).
| | | (relative error %) | (relative error %) | (relative error %) | (relative error %) | [39] (relative error %) |
| 0.01 | 6.2829757 | 6.28030856 (0.0424502) | 6.28297267 (0.0000482) | 6.28033909 (0.0419642) | 6.28297267 (0.0000482) | 6.2829757 (0.00000005) |
| 0.1 | 6.2622091 | 6.23585315 (0.42087294) | 6.26202447 (0.0029481) | 6.23646361 (0.4111248) | 6.26203439 (0.0027898) | 6.26220029 (0.0001407) |
| 10 | 0.7727359 | 0.75450185 (2.3596739) | 0.74930385 (3.032348) | 0.76075498 (1.5504538) | 0.77284969 (0.0147255) | 0.7564511 (2.1074) |
| 50 | 0.1561833 | 0.15271588 (2.2200941) | 0.15087022 (3.4018226) | 0.15400462 (1.3949487) | 0.15573888 (0.2845491) | 0.1527948 (2.1696) |
| 100 | 0.0781394 | 0.07642280 (2.1968399) | 0.07545104 (3.4404631) | 0.07706833 (1.3707164) | 0.07788792 (0.3218291) | 0.07644255 (2.1716) |
|
|