Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc-Gaussian Method

Table 2

The approximation 𝜆_𝑘,𝑁 and the exact solution 𝜆_𝑘 are all inside the interval [𝑎₋, 𝑎₊] for different values of 𝜀.

𝜆𝑘	Exact 𝜆𝑘	[𝑎−, 𝑎+], 𝜀=10^−2	[𝑎−, 𝑎+], 𝜀=10^−5	𝜆𝑘,𝑁
𝜆−2	−3.55825932025645	[−3.59648,−3.52003]	[−3.55829,−3.55822]	−3.5582593202564
𝜆−1	−1.98746299346156	[−2.02569,−1.94923]	[−1.98750,−1.98746]	−1.98746299346155
𝜆0	−0.41666666666666	[−0.454895,−0.37843]	[−0.416704,−0.416628]	−0.41666666666666
𝜆1	1.15412966012822	[1.115901,1.19235]	[1.15409,1.15416]	1.15412966012823
𝜆2	2.72492598692312	[2.68669,2.76315]	[2.72488,2.72496]	2.72492598692315

‖𝒰‖_∞=67.9396, 𝛽_𝑁(0)=1.2155.