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 iterationsAbsolute error in case of VIM after four iterations Absolute error in case of VIM after five iterations

−5−0.0005415497601−0.0005415497570−0.00054154976010.00000
−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