Approximation of Eigenvalues of Sturm-Liouville Problems by Using Hermite Interpolation

Table 7

For 𝑁=40, 𝑚=14 and 𝜃=1/26, the exact solution 𝜇_𝑘 are all inside the interval [𝑎₋, 𝑎₊] for different values of ε.

𝜇𝑘	𝜇1	𝜇2	𝜇3	𝜇4
Exact 𝜇𝑘	0.4828692021748484	1.966318052350425	4.827089429919572	7.919684444168381
ℐ𝜀,𝑁,, ε = 10^−5	[0.47918888, 0.48651557]	[1.96592879, 1.96670680]	[4.82707252, 4.82710633]	[7.91968171, 7.919687175]
ℐ𝜀,𝑁, ε = 10^−10	[0.48284084, 0.48289756]	[1.96631794, 1.96631815]	[4.82708919, 4.82708966]	[7.919684437, 7.919684450]

𝐸₁₀(ℱ_𝜃,𝑚)=2.83057×10¹⁸, 𝐸₉(ℱ_𝜃,𝑚)=1.12829×10¹⁴, 𝜈=1, 𝑀_ℱ𝜃,𝑚=1.57716×10⁷.