Theory and Modern Applications
Table 2 Comparison between analytical and numerical solutions of the Cahn–Allen equation to discuss the absolute error between both of them that explains the convergence between these solutions
From: Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation
Value of ℑ | Value of exact solution | Value of numerical solution | Value of absolute error |
|---|---|---|---|
0.00 | 0.5000000000 | 0.5000000000 | 2.220446049250313×10−16 |
0.10 | 0.5986876601 | 0.2413803205 | 0.3573073396 |
0.20 | 0.6899744811 | 0.1579706676 | 0.5320038135 |
0.30 | 0.7685247835 | 0.1843970897 | 0.5841276938 |
0.40 | 0.8320183851 | 0.2211480497 | 0.6108703354 |
0.50 | 0.8807970780 | 0.2798141133 | 0.6009829646 |
0.60 | 0.9168273035 | 0.3541465854 | 0.5626807182 |
0.70 | 0.9426758241 | 0.4561599710 | 0.4865158531 |
0.80 | 0.9608342772 | 0.5854048335 | 0.3754294438 |
0.90 | 0.9734030064 | 0.8229630569 | 0.1504399495 |
1.00 | 0.9820137900 | 0.9820137900 | 1.1102230246251565×10−16 |