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

Table 3

Regularization parameter 𝛼 and errors for Example 2 with 𝑘=5, 1% noise.

Θ	𝛼	‖𝑈^𝛿𝛼(𝛿)−𝑢‖𝐿2(∑)	‖𝑉^𝛿𝛼(𝛿)−𝜕𝑛𝑢‖𝐿2(∑)/‖𝜕𝑛𝑢‖𝐿2(∑)
𝜋/2	2.02×10^−2	1.79×10^−1	2.94×10^−1
𝜋	1.03×10^−4	5.99×10^−2	9.43×10^−2
3𝜋/2	3.81×10^−5	4.90×10^−3	1.96×10^−2