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

Table 11

For 𝑁=40, 𝑚=12, and 𝜃=1/14, 𝜇_𝑘 are all inside the interval [𝑎₋,𝑎₊] for different values of 𝜀.

𝜇𝑘	Exact 𝜇𝑘	[𝑎−,𝑎+], 𝜀=10^−6	[𝑎−,𝑎+], 𝜀=10^−12
𝜇1	0.58718716772603949302	[0.477526, 0.667764]	[0.586774, 0.587599]
𝜇2	1.67733212404977904702	[1.666867, 1.687341]	[1.677285, 1.677378]
𝜇3	3.05318927948461569256	[3.046882, 3.059372]	[3.053187, 3.053190]
𝜇4	4.64836948049457049728	[4.647491, 4.649246]	[4.64836924, 4.64836971]
𝜇5	6.22695152029019996978	[6.226707, 6.227195]	[6.22695140, 6.22695163]

ℰ₇(ℱ_𝜃,𝑚)=6.29794×10¹⁹, ℰ₆(ℱ_𝜃,𝑚)=4.70791×10¹⁸, 𝛼=1, and ℳ_ℱ𝜃,𝑚=4.71851×10¹².