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

Table 1

Regularization parameter 𝛼 and errors for Example 1 of Case 1 with 𝑘=3.

Noise	𝛼	‖𝑈^𝛿𝛼(𝛿)−𝑢‖𝐿2(∑)	‖𝑉^𝛿𝛼(𝛿)−𝜕𝑛𝑢‖𝐿2(∑)/‖𝜕𝑛𝑢‖𝐿2(∑)
0	7.78×10^−15	8.29×10^−4	3.6×10^−3
0.001	2.53×10^−6	2.20×10^−2	5.62×10^−2
0.01	2.08×10^−4	6.58×10^−2	1.21×10^−1
0.03	7.75×10^−4	8.53×10^−2	1.33×10^−1