Computation of eigenvalues of discontinuous dirac system using Hermite interpolation technique

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 7 For N = 20, m =5 and θ = 2/15, the approximation λ_k,Nand the exact solution λ_kare all inside the interval [a₋, a₊] for different values of ε

λ_kExact λ_k	[a₋, a₊], ε= 10⁻⁵	[a₋, a₊], ε= 10⁻¹⁰	λ _k,N
λ₋₂ −3.2964599324573105	[−3.402745, −3.177441]	[−3.305475, −3.286114]	−3.2964599325093795
λ₋₁ −1.725663605662414	[−1.840530, −1.615062]	[−1.749858, −1.702197]	−1.7256636055362218
λ₀ −0.15486727886751722	[−0.250393, −0.067671]	[−0.158786, −0.151287]	−0.15486727888681906
λ₁ 1.4159290479273794	[1.323736, 1.520703]	[1.408023, 1.424863]	1.4159290479703164
λ₂ 2.986725374722276	[2.863300, 3.109311]	[2.960260, 3.012514]	2.9867253745880475

$E_{4} (G_{θ, m}) = 319577, E_{3} (G_{θ, m}) = 48315.5, ℓ = 1, M_{G_{θ, m}} = 4400.77$