A Transformation Method for Solving Conservative Nonlinear Two-Degree-of-Freedom Systems

Table 3

RMSE values computed from the equivalent representation forms of (21) with 𝑢₁=−0.4, 𝑢₂=0.1, 𝑢₃=−0.01, and 𝑢₄=−0.315. Here 𝑏₁₁=1, 𝑏₁₂=𝑏₂₁=−𝛼²₂𝜎₁₀/(𝛽𝑧₁₀), 𝑏₂₂=𝛼²₂/𝛽, and 𝑑₁=−𝜀𝜎²₁₀.

𝜀	𝑦̈1+𝑎1𝑦1+𝑎2𝑦^31=0,; 𝑦̈2+𝑎3𝑦2=0.		𝑦̈1+𝑎1𝑦1+𝑎2𝑦^31=0,; 𝑦̈2+𝑏21𝑦1+𝑏22𝑦2=0.		𝑦̈2+𝑎3𝑦2=0,; 𝑦̈1+𝑏11𝑦1+𝑏12𝑦2+𝑑1𝑦^31=0.
	RMSE; 𝑦1(x)	RMSE; 𝑦2(x)	RMSE; 𝑦1(x)	RMSE; 𝑦2(x)	RMSE; 𝑦1(x)	RMSE; 𝑦2(x)
0.01	0.9448	1.3409	0.9448	2.3366	1.7724	1.3409
0.25	0.5880	1.2351	0.5880	1.1768	0.7684	1.2351
0.75	0.1609	1.0394	0.1609	0.1774	0.3309	1.0394
1.5	0.2402	0.7685	0.2402	0.2079	0.3157	0.7685
5	0.3637	0.4461	0.3637	0.1376	0.0910	0.4461
20	0.2489	0.3267	0.2489	0.0414	0.0125	0.3267
100	0.1226	0.2995	0.1226	0.0083	0.0011	0.2995