Advances in Artificial Neural Systems

Research Article

Comparison of Artificial Neural Network Architecture in Solving Ordinary Differential Equations

Table 3

Analytical and neural solutions with arbitrary- and regression-based weights (Example 2).


		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
0.1	1.0643	1.0900	1.0802	1.0910	1.0878	1.0923	1.0687
0.2	1.0725	1.1000	1.0918	1.0858	1.0715	1.0922	1.0812
0.3	1.0427	1.0993	1.0691	1.0997	1.0518	1.0542	1.0420
0.4	0.9885	0.9953	0.9732	0.9780	0.9741	0.8879	0.9851
0.5	0.9197	0.9208	0.9072	0.9650	0.9114	0.9790	0.9122
0.6	0.8433	0.8506	0.8207	0.8591	0.8497	0.8340	0.8082
0.7	0.7645	0.7840	0.7790	0.7819	0.7782	0.7723	0.7626
0.8	0.6864	0.7286	0.6991	0.7262	0.6545	0.6940	0.6844
0.9	0.6116	0.6552	0.5987	0.6412	0.6215	0.6527	0.6119
1.0	0.5413	0.5599	0.5467	0.5604	0.5341	0.5547	0.5445
1.1	0.4765	0.4724	0.4847	0.4900	0.4755	0.4555	0.4634
1.2	0.4173	0.4081	0.4035	0.4298	0.4202	0.4282	0.4172
1.3	0.3639	0.3849	0.3467	0.3907	0.3761	0.3619	0.3622
1.4	0.3162	0.3501	0.3315	0.3318	0.3274	0.3252	0.3100
1.5	0.2738	0.2980	0.2413	0.2942	0.2663	0.2773	0.2759
1.6	0.2364	0.2636	0.2507	0.2620	0.2439	0.2375	0.2320
1.7	0.2036	0.2183	0.2140	0.2161	0.2107	0.2177	0.1921
1.8	0.1749	0.2018	0.2007	0.1993	0.1916	0.1622	0.1705
1.9	0.1499	0.1740	0.1695	0.1665	0.1625	0.1512	0.1501
2.0	0.1282	0.1209	0.1204	0.1371	0.1299	0.1368	0.1245
2.1	0.1095	0.1236	0.1203	0.1368	0.1162	0.1029	0.1094
2.2	0.0933	0.0961	0.0942	0.0972	0.0949	0.0855	0.09207
2.3	0.0794	0.0818	0.0696	0.0860	0.0763	0.0721	0.0761
2.4	0.0675	0.0742	0.0715	0.0849	0.0706	0.0526	0.0640
2.5	0.0573	0.0584	0.0419	0.0609	0.0543	0.0582	0.0492
2.6	0.0485	0.0702	0.0335	0.0533	0.0458	0.0569	0.0477
2.7	0.0411	0.0674	0.0602	0.0581	0.0468	0.0462	0.0409
2.8	0.0348	0.0367	0.0337	0.0387	0.0328	0.0357	0.03460
2.9	0.0294	0.0380	0.0360	0.0346	0.0318	0.0316	0.0270
3.0	0.0248	0.0261	0.0207	0.0252	0.0250	0.0302	0.0247
3.1	0.0209	0.0429	0.0333	0.0324	0.0249	0.0241	0.0214
3.2	0.0176	0.0162	0.0179	0.0154	0.0169	0.0166	0.0174
3.3	0.0148	0.0159	0.0137	0.0158	0.0140	0.0153	0.0148
3.4	0.0125	0.0138	0.0135	0.0133	0.0130	0.0133	0.0129
3.5	0.0105	0.0179	0.0167	0.0121	0.0132	0.0100	0.0101
3.6	0.0088	0.0097	0.0096	0.0085	0.0923	0.0095	0.0090
3.7	0.0074	0.0094	0.0092	0.0091	0.0093	0.0064	0.0071
3.8	0.0062	0.0081	0.0078	0.0083	0.0070	0.0061	0.0060
3.9	0.0052	0.0063	0.0060	0.0068	0.0058	0.0058	0.0055
4.0	0.0044	0.0054	0.0052	0.0049	0.0049	0.0075	0.0046