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

Table 2

RMSE values computed by considering the canonical representation form of (13) with 𝜈₁=−9, 𝜈₂=−0.215, 𝜈₁₁=−2.325, and 𝜈₂₂=−8.5.

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	0.06010	0.0277	0.0044	0.0109	0.0606	0.0248
0.25	1.5351	0.6069	0.3611	0.2661	1.5824	0.4956
0.75	2.0910	0.8049	1.3988	0.6512	2.2351	0.7348
1.50	2.1222	0.8349	2.1151	0.8220	2.5577	1.1983
5	1.9552	0.8733	1.8608	0.8739	3.1331	8.8874
20	1.9116	0.9044	1.9889	0.9090	3.1549	8.7513
100	1.9495	0.9136	1.9704	0.9191	3.4887	8.1949