Research Article
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials
Table 1
The absolute and mean square errors using
for Sine-Gordon equation when n=m=2 and
.
| | X | VIM-Berns. | Exact | |
| | 0.1 | 0.397057362 | 0.396702532 | 3.548303×10−4 |
| | 0.2 | 0.391225182 | 0.390882208 | 3.429731×10−4 |
| | 0.3 | 0.381815965 | 0.381490269 | 3.256956×10−4 |
| | 0.4 | 0.369256745 | 0.368953065 | 3.036803×10−4 |
| | 0.5 | 0.354079776 | 0.353801996 | 2.777801×10−4 |
| | 0.6 | 0.336872278 | 0.336623332 | 2.489467×10−4 |
| | 0.7 | 0.318228605 | 0.318010464 | 2.1814014×10−4 |
| | 0.8 | 0.298710758 | 0.298524478 | 1.862801×10−4 |
| | 0.9 | 0.278820327 | 0.278666139 | 1.541880×10−4 |
| | 1.0 | 0.258982287 | 0.258859720 | 1.225671×10−4 |
| | MSE | | | 7.020528502×10−8 |
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