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
				𝑤(𝐴),𝑣(𝐴); (four nodes)	𝑤(𝑅),𝑣(𝑅); (four nodes)	𝑤(𝐴),𝑣(𝐴); (five nodes)	𝑤(𝑅),𝑣(𝑅); (five nodes)	𝑤(𝐴),𝑣(𝐴); (six nodes)	𝑤(𝑅),𝑣(𝑅); (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