Research Article
Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation
Table 2
Absolute error between the VIM solution and traveling wave solution at
and
.
| | Traveling wave solution () | Solution by VIM after four and five iterations | Absolute error in case of VIM after four iterations | Absolute error in case of VIM after five iterations | | |
| −5 | −0.0005415497601 | −0.0005415497570 | −0.0005415497601 | | 0.00000 | −4 | −0.001097714003 | −0.001097713996 | −0.001097713993 | | | −3 | −0.002223780506 | −0.002223780417 | −0.002223780437 | | | −2 | −0.004499794675 | −0.004499793394 | −0.004499794109 | | | −1 | −0.009084075273 | −0.009084065692 | −0.009084070631 | | | 0 | −0.01825307504 | −0.01825299748 | −0.01825303736 | | | 1 | −0.03633741749 | −0.03633679823 | −0.03633712022 | | | 2 | −0.07104238533 | −0.07103762964 | −0.07104015939 | | | 3 | −0.1342747341 | −0.1342406215 | −0.1342595369 | | | 4 | −0.2392905691 | −0.2390661759 | −0.2391995376 | | | 5 | −0.3894877140 | −0.3880553670 | −0.3889625354 | | |
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