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

Table 3

For 𝑁=15, 𝑚=10, and 𝜃=1/5, the exact solution 𝜇_𝑘 are all inside the interval [𝑏₋, 𝑏₊] for different values of ε.

𝜇𝑘	𝜇1	𝜇2	𝜇3	𝜇4
Exact 𝜇𝑘	1.0493258679653497	3.5207214555369464	6.505146961583527	9.578576417519093
ℐ𝜀,𝑁, 𝜀=10^−5	[1.04294069, 1.05557896]	[3.51981844, 3.52162396]	[6.50375768, 6.50653831]	[9.55222305, 9.60712093]
ℐ𝜀,𝑁, 𝜀=10^−10	[1.04932561, 1.049326118]	[3.52072141, 3.52072149]	[6.50514690, 6.50514702]	[9.57857529, 9.57857754]

𝐸₈(ℛ_𝜃,𝑚)=4.51845×10⁸, 𝐸₇(ℛ_𝜃,𝑚)=2.29709×10⁵, 𝜈=1, 𝑀_ℛ𝜃,𝑚=4.55609×10⁴.