On the Convergence of the Homotopy Analysis Method for Inner-Resonance of Tangent Nonlinear Cushioning Packaging System with Critical Components

Table 4

The residual errors ER_𝑋 and ER_𝑌 for various 𝑇∈(0,1).

𝑇	5-order		6-order
	ER𝑋	ER𝑌	ER𝑋	ER𝑌
0.1	7.65813×10^−11	1.37420×10^−9	3.18762×10^−13	4.47395×10^−11
0.2	3.06638×10^−10	2.43550×10^−8	1.76197×10^−14	4.84994×10^−11
0.3	1.58864×10^−10	8.87158×10^−8	3.49043×10^−12	1.21465×10^−9
0.4	2.05543×10^−9	5.62311×10^−7	9.40057×10^−12	7.36418×10^−10
0.5	2.20192×10^−9	1.18024×10^−6	7.17227×10^−11	1.31996×10^−8
0.6	1.04361×10^−8	6.66260×10^−7	5.64075×10^−11	4.10080×10^−8
0.7	5.15236×10^−8	3.16150×10^−7	6.52645×10^−10	1.44031×10^−8
0.8	1.17256×10^−7	1.07335×10^−5	2.96157×10^−9	2.22440×10^−7
0.9	1.17456×10^−7	1.27292×10^−5	4.99250×10^−9	5.66406×10^−7