Research Article
Treating Transcendental Functions in Partial Differential Equations Using the Variational Iteration Method with Bernstein Polynomials
Table 2
The absolute and mean square errors using
for Sine-Gordon equation when n=m=1 and
.
| | t | VIM-Berns. | Exact | |
| | 0.01 | 0.03980022977 | 0.03979951651 | 7.132600×10−7 |
| | 0.02 | 0.07959685852 | 0.07959115424 | 5.704280×10−6 |
| | 0.03 | 0.1193862874 | 0.1193670439 | 1.924350×10−5 |
| | 0.04 | 0.1591649208 | 0.1591193346 | 4.558630×10−5 |
| | 0.05 | 0.1989291693 | 0.1988402037 | 8.896560×10−5 |
| | 0.06 | 0.2386754506 | 0.2385218656 | 1.535849×10−4 |
| | 0.07 | 0.2784001917 | 0.2781565807 | 2.436109×10−4 |
| | 0.08 | 0.3180998309 | 0.3177366650 | 3.631659×10−4 |
| | 0.09 | 0.3577708202 | 0.3572544980 | 5.163222×10−4 |
| | 0.1 | 0.3974096254 | 0.3967025322 | 7.070931×10−4 |
| | MSE | | | 8.825264703×10−7 |
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