A New Approach for Linear Eigenvalue Problems and Nonlinear Euler Buckling Problem

Table 2

Comparison of the first eigenvalue and solutions of Example 3.1 using Taylor’s decomposition method, exact values, and Table 4 from [9], when 𝑛=0.

𝑥	HWSM	FDM	TDM	Exact	Errors of TDM	Errors of TDM	Errors of TDM
	(ℎ=1/16)	(ℎ=1/16)	(𝑝=3) (ℎ=1/16)		(𝑝=3) (ℎ=1/16)	(𝑝=4) (ℎ=1/8)	(𝑝=5) (ℎ=1/4)
0	0	0	0	0	0	0	0
0.0625	0.27521	0.278599	0.275999	0.275899	1.54𝐸−10	—	—
0.125	0.54181	0.541196	0.541196	0.541196	2.91𝐸−10	1.13𝐸−11	—
0.1875	0.78549	0.785695	0.785695	0.785695	3.93𝐸−10	—	—
0.25	1.00482	1	1	1	4.45𝐸−10	1.74𝐸−11	6.87𝐸−12
0.3125	1.17851	1.17588	1.17588	1.17588	4.37𝐸−10	—	—
0.375	1.31285	1.30656	1.30656	1.30656	3.61𝐸−10	1.41𝐸−11	—
0.4375	1.38376	1.38704	1.38704	1.38704	2.15𝐸−10	—	—
0.5	1.41103	1.41421	1.41421	1.41421	2.22𝐸−16	2.22𝐸−16	0
0.5625	1.38376	1.38704	1.38704	1.38704	2.76𝐸−10	—	—
0.625	1.31285	1.30656	1.30656	1.30656	6.03𝐸−10	2.35𝐸−11	—
0.6875	1.17851	1.17588	1.17588	1.17588	9.63𝐸−10	—	—
0.75	1.00482	1	1	1	1.33𝐸−9	5.22𝐸−11	2.06E-11
0.8125	0.78549	0.785695	0.785695	0.785695	1.70𝐸−9	—	—
0.875	0.54181	0.541196	0.541196	0.541196	2.03𝐸−9	7.96𝐸−11	—
0.9375	0.27521	0.275899	0.275999	0.275899	2.31𝐸−9	—	—
1	0	0	0	0	0	0	0

𝜆₁=10.9334 (HWSM), 10.8379 (FDM), 10.8696 (TDM), 10.8696 (Exact).