Numerical reconstruction of unknown boundary data in the Cauchy problem for Laplace's equation

This study explores an application of the quasi-solution and the Fourier methods used to solve a mixed initial-boundary problem involving Laplace's equation in a rectangle. The problem is reduced to a system consisting of mutually dependent direct and adjoint problems. The explicit formula for the quasi-solution is obtained using the Fourier method. Computational experiments are performed for different types of synthetic data, and admissible parameter ranges are established.