Comparison of Approximate Analytical and Numerical Solutions of the Allen Cahn Equation

Table 1

Absolute error between numerical results obtained by FDM, analytical solution obtained by using the tanh function method, and series solution obtained by VIM at .

	Numerical solution (FDM)	Tan hyperbolic functions solution	Solution by VIM after four and five iterations		Absolute error in case of FDM	Absolute error in case of VIM after four iterations	Absolute error in case of VIM after five iterations
			0.00	0.184247				0.184258	0.184163	0.184218
0.01	0.183187	0.183197	0.183105	0.183158
0.02	0.182131	0.182142	0.182051	0.182103
0.03	0.181080	0.181091	0.181002	0.181052
0.04	0.180034	0.180044	0.179957	0.180007
0.05	0.178992	0.179003	0.178917	0.178966
0.06	0.177955	0.177966	0.177882	0.177929