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

Table 12

For 𝑁=40, 𝑚=16, and 𝜃=1/12, 𝜇_𝑘 are all inside the interval [𝑎₋,𝑎₊] for different values of 𝜀.

𝜇𝑘	Exact 𝜇𝑘	[𝑎−,𝑎+], 𝜀=10^−7	[𝑎−,𝑎+], 𝜀=10^−12
𝜇1	0.58718716772603949302708573	[0.554227, 0.616993]	[0.587165, 0.587209]
𝜇2	1.67733212404977904702706192	[1.648191, 1.703225]	[1.6773305, 1.6773337]
𝜇3	3.05318927948461569256662121	[3.050775, 3.055585]	[3.05318912, 3.05318943]
𝜇4	4.64836948049456789592198501	[4.647994, 4.648743]	[4.648369468, 4.648369492]
𝜇5	6.2269515202901999697647050	[6.226831, 6.227072]	[6.226951509, 6.226951531]

ℰ₁₁(ℱ_𝜃,𝑚)=1.67235×10²⁴, ℰ₁₀(ℱ_𝜃,𝑚)=1.44089×10²³, 𝛼=1, and ℳ_ℱ𝜃,𝑚=1.28771×10¹³.