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

Table 7

Comparison of the exact eigenvalues with approximate eigenvalues obtained from Numerov’s method (Λ_𝑘) with correction and TDM (𝜇_𝑘) for Example 3.3 corresponding to 𝛽=10.

𝑘	𝜆𝑘	𝜆𝑘−Λ𝑘^(40)	𝜆𝑘−Λ𝑘^(80)	𝜆𝑘−𝜇𝑘^70	𝜆𝑘−𝜇𝑘^80
1	0.0000000	2.32𝐸−3	1.43𝐸−4	3.63𝐸−3	7.60𝐸−5
2	37.7596285	7.52𝐸−3	4.42𝐸−4	9.15𝐸−4	3.81𝐸−6
3	37.8059002	1.61𝐸−3	9.93𝐸−5	5.66𝐸−7	1.12𝐸−7
4	37.8525995	6.88𝐸−3	4.43𝐸−4	8.97𝐸−4	3.85𝐸−5
5	70.5475097	3.22𝐸−2	1.97𝐸−3	1.57𝐸−2	3.74𝐸−4
6	92.6538177	2.25𝐸−2	1.37𝐸−3	2.25𝐸−3	2.20𝐸−5
7	96.2058159	1.20𝐸−2	7.28𝐸−4	2.18𝐸−3	1.78𝐸−4
8	102.254347	3.45𝐸−2	2.09𝐸−3	4.38𝐸−3	2.44𝐸−4

ℎ=𝜋 for Taylor’s decomposition method.