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

Table 4

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	−3.29645993245731	[−3.322822,−3.270097]	[−3.296486,−3.296433]	−3.29645993245735
𝜆−1	−1.7256636056624	[−1.752025,−1.699301]	[−1.725689,−1.725637]	−1.7256636056621
𝜆0	−0.154867278867517	[−0.181229,−0.128505]	[−0.154893,−0.1548409]	−0.154867278867127
𝜆1	1.41592904792737	[1.389566,1.442291]	[1.415902,1.415955]	1.41592904792752
𝜆2	2.9867253747222	[2.960363,3.013087]	[2.986699,3.013087]	2.98672537472225

‖𝒰‖_∞=531.544, 𝛽_𝑁(0)=1.22382.