Research Article
Comparison of Artificial Neural Network Architecture in Solving Ordinary Differential Equations
Table 4
Analytical and neural solutions with arbitrary- and regression-based weights (Example
3).
| Input data |
Analytical |
Euler |
Runge-Kutta | Neural results | (four nodes) | (four nodes) | (five nodes) | (five nodes) | (six nodes) | (six nodes) |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.1 | 0.0671 | 0.1000 | 0.0671 | 0.0440 | 0.0539 | 0.0701 | 0.0602 | 0.0565 | 0.0670 | 0.2 | 0.0905 | 0.1241 | 0.0904 | 0.0867 | 0.0938 | 0.0877 | 0.0927 | 0.0921 | 0.0907 | 0.3 | 0.0917 | 0.1169 | 0.0917 | 0.0849 | 0.0926 | 0.0889 | 0.0932 | 0.0931 | 0.0918 | 0.4 | 0.0829 | 0.0991 | 0.0829 | 0.0830 | 0.0876 | 0.0806 | 0.0811 | 0.0846 | 0.0824 | 0.5 | 0.0705 | 0.0797 | 0.0705 | 0.0760 | 0.0748 | 0.0728 | 0.0714 | 0.0717 | 0.0706 | 0.6 | 0.0578 | 0.0622 | 0.0577 | 0.0492 | 0.0599 | 0.0529 | 0.0593 | 0.0536 | 0.0597 | 0.7 | 0.0461 | 0.0476 | 0.0461 | 0.0433 | 0.0479 | 0.0410 | 0.0453 | 0.0450 | 0.0468 | 0.8 | 0.0362 | 0.0360 | 0.0362 | 0.0337 | 0.0319 | 0.0372 | 0.0370 | 0.0343 | 0.0355 | 0.9 | 0.0280 | 0.0271 | 0.0280 | 0.0324 | 0.0308 | 0.0309 | 0.0264 | 0.0249 | 0.0284 | 1.0 | 0.0215 | 0.0203 | 0.0215 | 0.0304 | 0.0282 | 0.0255 | 0.0247 | 0.0232 | 0.0217 |
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