Computing Eigenvalues of Discontinuous Sturm-Liouville Problems with Eigenparameter in All Boundary Conditions Using Hermite Approximation

Table 6

For 𝑁=20, 𝑚=12; and 𝜃=1/4, 𝜇_𝑘 are all inside the interval [𝑎₋,𝑎₊] for different values of 𝜀.

𝜇𝑘	Exact 𝜇𝑘	[𝑎−,𝑎+], 𝜀=10^−5	[𝑎−,𝑎+], 𝜀=10^−10
𝜇1	0.57960311481097786078	[0.130168, 0.796074]	[0.579579, 0.579627]
𝜇2	1.78498389488883561160	[1.699182, 1.859482]	[1.784963, 1.785004]
𝜇3	3.23864734975141899542	[3.194355, 3.282835]	[3.238636, 3.238658]
𝜇4	4.77056233559052749760	[4.698242, 4.851169]	[4.770489, 4.770635]
𝜇5	6.32570436467225155153	[6.287476, 6.368771]	[6.325701, 6.325707]

ℰ₇(ℱ_𝜃,𝑚)=2.25863×10¹³, ℰ₆(ℱ_𝜃,𝑚)=5.91004×10¹², 𝛼=1, and ℳ_ℱ𝜃,𝑚=2.11965×10⁹.