An Integral Equations Method for the Cauchy Problem Connected with the Helmholtz Equation

Table 4

Regularization parameter 𝛼 and errors for Example 2 with 𝑘=5, 3% noise.

Θ	𝛼	‖𝑈^𝛿𝛼(𝛿)−𝑢‖𝐿2(∑)	‖𝑉^𝛿𝛼(𝛿)−𝜕𝑛𝑢‖𝐿2(∑)/‖𝜕𝑛𝑢‖𝐿2(∑)
𝜋/2	4.04×10^−2	2.32×10^−1	3.13×10^−1
𝜋	3.13×10^−4	7.37×10^−2	1.19×10^−1
3𝜋/2	1.54×10^−4	1.83×10^−2	5.79×10^−2