Research Article
Comparison of Artificial Neural Network Architecture in Solving Ordinary Differential Equations
Table 5
Analytical and neural solutions with arbitrary- and regression-based weights (Example
4).
| | | Neural results | Input data | Analytical | | | | | | | | | (four nodes) | (four nodes) | (five nodes) | (five nodes) | (six nodes) | (six nodes) |
| 0 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 0.1000 | 1.1052 | 1.1069 | 1.1061 | 1.1093 | 1.1060 | 1.1075 | 1.1051 | 0.2000 | 1.2214 | 1.2337 | 1.2300 | 1.2250 | 1.2235 | 1.2219 | 1.2217 | 0.3000 | 1.3499 | 1.3543 | 1.3512 | 1.3600 | 1.3502 | 1.3527 | 1.3498 | 0.4000 | 1.4918 | 1.4866 | 1.4921 | 1.4930 | 1.4928 | 1.4906 | 1.4915 | 0.5000 | 1.6487 | 1.6227 | 1.6310 | 1.6412 | 1.6456 | 1.6438 | 1.6493 | 0.6000 | 1.8221 | 1.8303 | 1.8257 | 1.8205 | 1.8245 | 1.8234 | 1.8220 | 0.7000 | 2.0138 | 2.0183 | 2.0155 | 2.0171 | 2.0153 | 2.0154 | 2.0140 | 0.8000 | 2.2255 | 2.2320 | 2.2302 | 2.2218 | 2.2288 | 2.2240 | 2.2266 | 0.9000 | 2.4596 | 2.4641 | 2.4625 | 2.4664 | 2.4621 | 2.4568 | 2.4597 | 1.0000 | 2.7183 | 2.7373 | 2.7293 | 2.7232 | 2.7177 | 2.7111 | 2.7186 |
|
|