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

Table 4

RMSE values computed by considering the canonical representation form of (21) with 𝜈₁=0.85, 𝜈₂=0.45, 𝜈₁₁=−0.01, and 𝜈₂₂=0.1.

𝜀	𝑢̈1+𝑏1𝑢1+𝑏2𝑢^31=0,; 𝑢̈2+𝑏3𝑢2+𝑏4𝑢^32=0.		𝑢̈1+𝑏1𝑢1+𝑏2𝑢^31=0,; 𝑢̈2+𝜔^2𝑛2𝑢2+𝜀{𝜑5𝑢^31+𝜑6𝑢^21𝑢2+𝜑7𝑢1𝑢^22+𝜑8𝑢^32}=0.		𝑢̈2+𝑏3𝑢2+𝑏4𝑢^32=0,; 𝑢̈1+𝜔^2𝑛1𝑢1+𝜀{𝜑1𝑢^31+𝜑2𝑢^21𝑢2+𝜑3𝑢1𝑢^22+𝜑4𝑢^32}=0.
	RMSE; 𝑢1(x)	RMSE; 𝑢2(x)	RMSE; 𝑢1(x)	RMSE; 𝑢2(x)	RMSE; 𝑢1(x)	RMSE; 𝑢2(x)
0.01	0.0077	0.0168	0.0066	0.0174	0.0028	0.0050
0.25	0.1953	0.3769	0.1325	0.3596	0.1516	0.2393
0.75	0.8844	1.2761	0.7365	1.1609	0.9850	0.9016
1	1.0156	1.3704	0.9953	1.4230	1.4544	3.8230
1.5	0.8727	1.1634	0.9922	1.3683	1.5028	4.3001
5	0.9301	1.2149	0.9678	1.4201	0.8801	4.0894
20	0.9010	1.2577	0.9729	1.5285	1.2238	3.8974
100	0.9282	1.270	1.0162	1.5621	1.2479	3.8438