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

Table 8

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=20.

𝑘	𝜆𝑘	𝜆𝑘−Λ𝑘^(40)	𝜆𝑘−Λ𝑘^(80)	𝜆𝑘−𝜇𝑘^100	𝜆𝑘−𝜇𝑘^110
1	0.0000000	1.93𝐸−2	1.17𝐸−3	1.04𝐸−1	7.64𝐸−3
2	77.9161943	1.22𝐸−1	7.38𝐸−3	4.37𝐸−2	6.98𝐸−2
3	77.9161957	1.63𝐸−2	9.95𝐸−4	9.89𝐸−4	1.67𝐸−4
4	77.9161972	1.62𝐸−2	9.89𝐸−4	1.13𝐸−1	7.48𝐸−2
5	151.463224	3.90𝐸−1	2.33𝐸−2	7.04𝐸−1	1.56𝐸−1

ℎ=𝜋 for Taylor’s decomposition method.